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Call number: | 9783319497631:ONLINE Show nearby items on shelf |
Title: | Geometry Over Nonclosed Fields |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (IX, 261 p. 3 illus., 1 illus. in color p.) |
Contents: | Preface -- On the Kobayashi pseudometric, complex automorphisms and hyperahler manifolds by Fedor Bogomolov, Ljudmila Kamenova, Steven Lu, and Misha Verbitsky -- Lines on cubic hypersurfaces over finite fields by Olivier Debarre, |
Antonio Laface, and Xavier Roulleau -- Perverse sheaves of categories and non-rationality by Andrew Harder, Ludmil Katzarkov, and Yijia Liu -- Divisor classes and the virtual canonical bundle for genus zero maps by A. J. de Jong and | |
Jason Starr -- A stronger derived Torelli theorem for K3 surfaces by Max Lieblich and Martin Olsson -- Morphisms to Brauer-Severi varieties, with applications to del Pezzo surfaces by Christian Liedtke -- Arithmetic of K3 surfaces by | |
Anthony Varilly-Alvarado -- One-dimensional cohomology with finite coefficients and roots of unity by Yuri G. Zarhin | |
ISBN: | 9783319497631 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Mathematics , Algebraic Geometry |
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Call number: | 9783319393391:ONLINE Show nearby items on shelf |
Title: | Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) |
Contents: | Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic |
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular | |
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded | |
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces | |
ISBN: | 9783319393391 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9789811009167:ONLINE Show nearby items on shelf |
Title: | Geometry of Cauchy-Riemann Submanifolds |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (390 p.) |
Note: | 10.1007/978-981-10-0916-7 |
Contents: | Chapter 1. CR-warped submanifolds in Kaehler manifolds -- Chapter 2. CR Submanifolds and -invariants -- Chapter 3. CR Submanifolds of the nearly Kahler 6-sphere -- Chapter 4. CR submanifolds of Hermitian manifolds and the tangential C-R equations - - Chapter 5. CR Submanifolds in (l.c.a.) Kaehler and S-manifolds -- Chapter 6. Lorentzian geometry and CR submanifolds -- Chapter 7. Submanifolds in holomorphic statistical manifolds -- Chapter 8. CR Submanifolds in complex and Sasakian space forms -- Cha pter 9. CR-Doubly warped product submanifolds -- Chapter 10. Ideal CR submanifolds -- Chapter 11. Submersions of CR submanifolds -- Chapter 12. CR Submanifolds of semi-Kaehler manifolds -- Chapter 13. Paraquaternionic CR submanifolds |
ISBN: | 9789811009167 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Convex geometry , Discrete geometry , Differential geometry , Mathematical physics , Mathematics , Differential Geometry , Mathematical Physics , Convex and Discrete Geometry |
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Call number: | SPRINGER-2016-9784431560210:ONLINE Show nearby items on shelf |
Title: | Geometry and Topology of Manifolds 10th China-Japan Conference 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (10 p.) |
Note: | 10.1007/978-4-431-56021-0 |
ISBN: | 9784431560210 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 154 |
Keywords: | Mathematics , Partial differential equations , Differential geometry , Manifolds (Mathematics) , Complex manifolds , Mathematics , Differential Geometry , Manifolds and Cell Complexes (incl. Diff.Topology) , Partial Differential Equations |
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Call number: | SPRINGER-2016-9783662493618:ONLINE Show nearby items on shelf |
Title: | Topologie algébrique Chapitres 1 à 4 |
Author(s): |
N Bourbaki |
Date: | 2016 |
Size: | 1 online resource (498 p.) |
Note: | 10.1007/978-3-662-49361-8 |
Contents: | Mode d'Emploi -- Introduction -- Chapitre I. Revêtements -- 1. Produits fibrés et carrés cartésiens -- 2. Applications étales -- 3. Faisceaux -- 4. Revêtements -- 5. Revêtements principaux -- 6. Espaces simplement connexes -- Exercices -- Ch apitre II. Groupoïdes -- 1. Carquois -- 2. Graphes -- 3. Groupoïdes -- 4. Homotopies -- 5. Coégalisateur -- Exercices -- Chapitre III. Homotopie et Groupoïdes de Poincaré -- 1. Homotopies, homéotopies -- 2. Homotopie et chemins -- 3. Groupoïde de P oincaré -- 4. Homotopie et revêtements -- 5. Homotopie et revêtements (cas des espaces localement connexes par arcs) -- Exercices -- Chapitre IV. Espaces Delaçables -- 1. Espaces délaçables -- 2. Groupes de Poincaré des espaces délaçables -- 3. G roupes de Poincaré des groupes topologiques -- 4. Théorie de la descente -- 5. Théorème de van Kampen -- 6. Espaces classifiants -- Exercices -- Index des notations -- Index terminologique |
ISBN: | 9783662493618 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Group theory , Algebraic topology , Manifolds (Mathematics) , Complex manifolds , Mathematics , Algebraic Topology , Category Theory, Homological Algebra , Manifolds and Cell Complexes (incl. Diff.Topology) , Group Theory and Generalizations |
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Call number: | SPRINGER-2016-9783319313382:ONLINE Show nearby items on shelf |
Title: | Essays in Mathematics and its Applications In Honor of Vladimir Arnold |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (22 p.) |
Note: | 10.1007/978-3-319-31338-2 |
Contents: | A new way to compute the Rodrigues coefficients of functions of the Lie groups of matrices (D. Andrica, O.L. Chender) -- Quasimodes in integrable systems and semi-classical limit (M. Baldo, F. Raciti) -- Manifolds which are complex and symplectic bu t not Kahler (G. Bazzoni, V. Munoz) -- Solvability of a non clamped frictional contact problem with adhesion (O. Chau, D. Goeleven, R. Oujja) -- The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence (A. Fortunati, S. Wi ggins) -- Iterative Methods for the Elastography Inverse Problem of Locating Tumors (B. Jadamba, A.A. Khan, F. Raciti, C. Tammer, B. Winkler) -- Transversality theory with applications to differential equations (D. Motreanu, V.V. Motreanu) -- Lattice-like subsets of Euclidean Jordan algebras (A.B. Nemeth, S.Z. Nemeth) -- Simultaneous Diophantine approximation: Searching for analogues of Hurwitz’ theorem (W.G. Nowak) -- On the fixed points of a Hamiltonian diffeomorphism in presence of |
fundamental group (K. Ono, A. Pajitnov) -- Some Generalizations of Fixed Point Theorems on S-Metric Spaces (N.Y. Ozgur, N.A. Tas) -- Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces (C. Park, J.R. Lee, T.M. Rassias) -- The Maslov Ind ex in PDEs Geometry (A. Prastaro) -- On the infimum of certain functionals (B. Ricceri) -- The Algebra of Gyrogroups: Cayley Theorem, Lagrange Theorem, and Isomorphism Theorems (T. Suksumran) -- Mild continuity properties of relations and relators in rela tor spaces (A. Szaz, A. Zakaria) -- Contraction Maps in Pseudometric Structures (M. Turinici) -- Novel Tools to Determine Hyperbolic Triangle Centers (A.A. Ungar) | |
ISBN: | 9783319313382 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Dynamics , Ergodic theory , Global analysis (Mathematics) , Manifolds (Mathematics) , Algebraic topology , Complex manifolds , Mathematics , Dynamical Systems and Ergodic Theory , Algebraic Topology , Manifolds and Cell Complexes (incl. Diff.Topology) , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2016-9783319312811:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis, Approximation Theory and Their Applications |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (20 p.) |
Note: | 10.1007/978-3-319-31281-1 |
Contents: | A brief history of the Favard operator and its variants -- Bivariate extension of linear positive operators -- Positive Green’s Functions for Boundary Value Problems with Conformable Derivatives -- The retraction-displacement condition in the theo ry of fixed point equation with a convergent iterative algorithm -- An adaptive finite element method for solving a free boundary problem with periodic boundary conditions in lubrication theory -- Evolution solutions of equilibrium problems - a computatio nal approach -- Cantor, Banach and Baire theorems in generalized metric spaces -- A Survey of Perturbed Ostrowski Type Inequalities -- Hyers-Ulam-Rassias stability of the generalized Wilson’s functional equation -- Approximation under Exponential Growth Conditions by Szász and Baskakov Type Operators in the Complex Plane -- On the asymptotic behavior of sequences of positive linear approximation operators -- Approximation of functions by additive and by quadratic mappings -- Bernstein Type |
Inequalities concerning Growth of Polynomials -- Approximation for generalization of Baskakov-Durrmeyer operators -- A Tour on p (x)-Laplacian Problems When p = ∞ -- An umbral calculus approach to Bernoulli-Padé polynomials -- Hadamard Matrices: Insights into their growth factor and determinant computations -- Localized summability kernels for Jacobi expansions -- Quadrature rules with multiple nodes -- A -summability of sequences of linear conservative operators -- Simultaneous Weighted Approxim ation with Multivariate Baskakov-Schurer Operators -- Approximation of Discontinuous Functions by q-Bernstein Polynomials -- Nests, and their Role in the Orderability Problem -- Resolvent Operators for Some Classes of Integro-Differential Equations -- Com ponent Matrices of a Square Matrix and their Properties -- Solutions of Some Types of Differential Equations and of Their Associated Physical Problems by Means of Inverse Differential Operators -- A modified pointwise estimate on simultaneous | |
approximation by Bernstein polynomials -- Structural Fixed Point Results in Metric Spaces -- Models of Fuzzy Linear Regression: An Application in Engineering -- Properties of Functions of generalized bounded variations | |
ISBN: | 9783319312811 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Optimization and Its Applications: 111 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Operator theory , Special functions , Computer mathematics , Calculus of variations , Mathematics , Calculus of Variations and Optimal Control Optimization , Operator Theory , Special Functions , Global Analysis and Analysis on Manifolds , Computational Mathematics and Numerical Analysis |
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Call number: | SPRINGER-2016-9783319281865:ONLINE Show nearby items on shelf |
Title: | Convexity and Discrete Geometry Including Graph Theory Mulhouse, France, September 2014 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (39 p.) |
Note: | 10.1007/978-3-319-28186-5 |
Contents: | Introduction -- PART I Research Articles. Marcus: Tudor Zamfirescu: from convex to magic -- Yuan: Acute Triangulations of Rectangles, with Angles Bounded Below -- Skupien: Multi-compositions in exponential counting of hypohamiltonian snarks -- Shabb ir & T. Zamfirescu: Hamiltonicity in k-tree-Halin graphs -- Schneider: Reflections of planar convex bodies -- Rouyer: Steinhaus conditions for convex polyhedra -- Riviere: About the Hausdorff dimension of the set of endpoints of convex surfaces -- Prunesc u: About a surprising computer program of Matthias Müller -- Oliveros, Martinez & Montejano: Extremal results on intersection graphs of boxes in R^d -- Massé, Euler & Lemarchand: On the connected spanning cubic subgraph problem -- Kincses: On the Helly dimension of Hanner polytopes -- Itoh & Ohtsuka: Classification of normal 2-polyhedra of positive constant curvature -- Heppes & Jeronimo-Castro: T(4) families ofϕ-disjoint ovals -- Fruchard & Magazinov: Fair partitioning by straight lines -- |
Filip & Petrusel: Fixed point theorems for multivalued Zamfrescu operators in convex Kasahara spaces -- Et-Taoui: Complex conference matrices, complex Hadamard matrices and complex equiangular tight frames -- Chevallier, Fruchard & Vilcu: Envelopes of α-sections -- Bokowski & al.: Selected open and solved problems in computational synthetic geometry -- Bau: Reductions of 3-connected quadrangulations of the sphere -- Barany & Por: Paths on the sphere without small angles -- PART II Open Problem Note s. Zamfirescu T.: Two problems on cages for discs -- Zamfirescu Carol T.: Seven problems on hypohamiltonian and almost hypohamiltonian graphs -- Vilcu & Zamfirescu: Six problems on the length of the cut locus -- Simoes-Pereira: Existence Problems for Matr oidal Families -- Funar: Cubical Pachner moves -- Eckhoff: Problems in Discrete Geometry -- Chevallier & Fruchard: What is the minimal cardinal of a family which shatters all d-subsets of a finite set? -- Baskoro: Some open problems of Ramsey | |
minimal graphs. | |
ISBN: | 9783319281865 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 148 |
Keywords: | Mathematics , Global analysis (Mathematics) , Manifolds (Mathematics) , Convex geometry , Discrete geometry , Combinatorics , Graph theory , Mathematics , Convex and Discrete Geometry , Graph Theory , Combinatorics , Global Analysis and Analysis on Manifolds |
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Call number: | SPRINGER-2014-9783319052540:ONLINE Show nearby items on shelf |
Title: | Trends in Contemporary Mathematics [electronic resource] |
Author(s): |
Vincenzo Ancona Elisabetta Strickland |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book covers a wide spectrum of hot topics and current trends in mathematics, including noncommutative algebra via deformation theory, optimal transportation, nonlinear potential theory,kinetic theory and gas dynamics,geometric numerical integrat ion, finite simple groups of small essential dimension, optimal control problems, extended Dynkin diagrams, spin glasses, aspherical closed manifolds, Boltzmann systems, birational geometry of projectivevarieties and directed graphs, nonlinear diffusion, geometric constructions of extremal metrics on complex manifolds, and Pells equation in polynomials. The book comprises a selection of contributions by leading internationalmathematicians who were speakers at the INdAM Day, an initiative dating back to 20 04 at which the most recent developments in contemporary mathematics are presented |
Contents: | 1 F. Guerra: Interpolation and comparison methods in the mean field spin glass model |
2 A. De Sole, V.G. Kac, D. Valeri: Integrability of dirac reduced Bi | |
Hamiltonian equations | |
3 W. Luck: Some open problems about aspherical closed manifolds abstract | |
4 P. Etingof: Exploring noncommutative algebras via deformation theory | |
5 G. Lancia: Mathematical models and solutions for the analysis of human genotypes | |
6 M. Manetti: Kodaira | |
Spencer formality of products of complex manifolds | |
7 O. Debarre, B. Lass: Monomial transformations of the projective space | |
8 J.L. Vazquez: Progress in the | |
ISBN: | 9783319052540 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Differential equations, partial , Computer science Mathematics |
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Call number: | SPRINGER-2014-9783319024417:ONLINE Show nearby items on shelf |
Title: | Cohomological Aspects in Complex Non-Khler Geometry [electronic resource] |
Author(s): |
Daniele Angella |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | In these notes, we provide a summary of recentresults on the cohomological properties of compact complex manifolds not endowed with a Khler structure. On the one hand, the large number of developed analytic techniques makes itpossible to prove strong cohomological properties for compact Khler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Khler structure. Wefocus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers tostudy explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered |
Contents: | Preliminaries on (almost |
) complex manifolds | |
Cohomology of complex manifolds | |
Cohomology of nilmanifolds | |
Cohomology of almost | |
complex manifolds | |
References | |
ISBN: | 9783319024417 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2095 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783319008196:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Khler-Ricci Flow [electronic resource] |
Author(s): |
Sebastien Boucksom Philippe Eyssidieux Vincent Guedj |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Khler-Ricci flow and its current state-of-the-art. Whileseveral excellent books on Khler-Einstein geometry are available, there have been no such works on the Khler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differentialgeometry, complex algebraic geometry and Riemannian geom etry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is centralin G. Perelmans celebrated proof of the Poincar conjecture. When specialized f or Khler manifolds, it becomes the Khler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampre equation). As a spin-off of hisbreakthrough, G. Perelman proved the convergence of the Khler-Ricci flow on Khler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelmansideas: the Khler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contracti ons assume the role of Perelmans surgeries |
Note: | Springer eBooks |
Contents: | The (real) theory of fully non linear parabolic equations |
The KRF on positive Kodaira dimension Khler manifolds | |
The normalized Khler | |
Ricci flow on Fano manifolds | |
Bibliography | |
ISBN: | 9783319008196 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2086 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2013-9783319001289:ONLINE Show nearby items on shelf |
Title: | Hypoelliptic Laplacian and BottChern Cohomology [electronic resource] : A Theorem of RiemannRochGrothendieck in Complex Geometry |
Author(s): |
Jean-Michel Bismut |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes inBottChern cohomology, which is a refi nement for complex manifolds of de Rham cohomology. When the manifolds are Khler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformationvia Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKeanSinger in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.Onetool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for thedeformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Whil e the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonicoscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea dev eloped in the book is that while classical elliptic Hodge theory is based on theHermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an imp ortant role, either as a motivation of some constructions,or in the proofs themselves |
Note: | Springer eBooks |
Contents: | Introduction |
1 The Riemannian adiabatic limit | |
2 The holomorphic adiabatic limit | |
3 The elliptic superconnections | |
4 The elliptic superconnection forms | |
5 The elliptic superconnections forms | |
6 The hypoelliptic superconnections | |
7 The hypoelliptic superconnection forms | |
8 The hypoelliptic superconnection forms of vector bundles | |
9 The hypoelliptic superconnection forms | |
10 The exotic superconnection forms of a vector bundle | |
11 Exotic superconnections and RiemannRochGrothendieck | |
Bibliography | |
Subject Index | |
Index of Notation. | |
ISBN: | 9783319001289 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf |
Title: | Complex Kleinian Groups [electronic resource] |
Author(s): |
Angel Cano Juan Pablo Navarrete Jos Seade |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Acknowledgments | |
1 A glance of the classical theory | |
2 Complex hyperbolic geometry | |
3 Complex Kleinian groups | |
4 Geometry and dynamics of automorphisms of P2C | |
5 Kleinian groups with a control group | |
6 The limit set in dimension two | |
7 On the dynamics of discrete subgroups of PU(n,1) | |
8 Projective orbifolds and dynamics in dimension two | |
9 Complex Schottky groups | |
10 Kleinian groups and twistor theory | |
Bibliography | |
Index. | |
ISBN: | 9783034804813 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v303 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial |
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Call number: | SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf |
Title: | Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday |
Author(s): |
Alan Huckleberry Ivan Penkov Gregg Zuckerman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted |
Note: | Springer eBooks |
Contents: | Preface |
Real group orbits on flag manifolds | |
Complex connections with trivial holonomy | |
Indefinite harmonic theory and harmonic spinors | |
Twistor theory and the harmonic hull | |
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets | |
Propagation of the multiplicity | |
freeness property for holomorphic vector bundles | |
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains | |
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf | |
Weakly harmonic Maa forms and the princi | |
ISBN: | 9781461471936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v306 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2012-9783642244407:ONLINE Show nearby items on shelf |
Title: | Quantum Triangulations [electronic resource] : Moduli Spaces, Strings, and Quantum Computing |
Author(s): |
Mauro Carfora Annalisa Marzuoli |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemannmoduli space theory, str ings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physicaltheories are typically formulated, but their appear ance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a waywhich makes manifest the basic geometric structures of the physical intera ctions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physicaltheory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of casesstudies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied m athematicians and theoretical physicists working in the field of quantum geometry and its applications. |
Note: | Springer eBooks |
Contents: | Triangulated Surfaces and Polyhedral Structures |
Singular Euclidean Structures an Riemann Surfaces | |
Polyhedral Surfaces and the Weil | |
Petersson Form | |
The Quantum Geometry of Polyhedral Surfaces | |
State Sum Models and Observables | |
Combinatorial Framework for Topological Quantum Computing | |
A Capsule of Moduli Space Theory | |
Spectral Theory on Polyhedral Surfaces | |
Index | |
ISBN: | 9783642244407 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v845 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Cell aggregation Mathematics , Quantum theory |
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Call number: | SPRINGER-2012-9783642236693:ONLINE Show nearby items on shelf |
Title: | Complex MongeAmpre Equations and Geodesics in the Space of Khler Metrics [electronic resource] |
Author(s): |
Vincent Guedj |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpre operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Khler manifolds(with or without boundary). The se operators are of central use in several fundamental problems of complex differential geometry (KhlerEinstein equation, uniqueness of constant scalar curvature metrics), complex analysis anddynamics. The topics covered include, the Dirichlet problem (af ter BedfordTaylor), MongeAmpre foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation ofKrylov regularity results, a modernized proof of the CalabiYau theorem (after Yau and Kolod ziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Khler metrics (after Mabuchi, Semmesand Donaldson), generalizations of the regularity theory of CaffarelliKohnNirenbergSpruck (after Guan, Chen and Block i) and Bergman approximation of geodesics (after PhongSturm and Berndtsson). Each chapter can be readindependently and is based on a series of lectures byR. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non -experts. The book is thus addressed to any mathematician with some interest inone of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis |
Note: | Springer eBooks |
Contents: | 1.Introduction |
I. The Local Homogenious Dirichlet Problem | |
2. Dirichlet Problem in Domains of Cn | |
3. Geometric Maximality | |
II. Stochastic Analysis for the Monge | |
Ampre Equation | |
4. Probabilistic Approach to Regularity | |
III. Monge | |
Ampre Equations on Compact Manifolds | |
5.The Calabi | |
Yau Theorem | |
IV Geodesics in the Space of Khler Metrics | |
6. The Riemannian Space of Khler Metrics | |
7. MA Equations on Manifolds with Boundary | |
8. Bergman Geodesics | |
ISBN: | 9783642236693 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2038 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2012-9783642236471:ONLINE Show nearby items on shelf |
Title: | Milnor Fiber Boundary of a Non-isolated Surface Singularity [electronic resource] |
Author(s): |
Andrs Nmethi gnes Szilrd |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
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Note: | Springer 2013 e-book collections |
Note: | In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in threevariables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides thecharacteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS.Moreover, the horizontal and vertical monodromies of the transversal type singu larities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples,including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 The topology of a hypersurface germ f in three variables Milnor fiber | |
3 The topology of a pair (f g) | |
4 Plumbing graphs and oriented plumbed 3 | |
manifolds | |
5 Cyclic coverings of graphs | |
6 The graph GC of a pair (f g). The definition | |
7 The graph GC . Properties | |
8 Examples. Homogeneous singularities | |
9 Examples. Families associated with plane curve singularities | |
10 The Main Algorithm | |
11 Proof of the Main Algorithm | |
12 The Collapsing Main Algorithm | |
13 Vertical/horizontal monodromies | |
14 The algebraic monodromy of H1( F). Starting point | |
15 T | |
ISBN: | 9783642236471 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2037 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Algebraic topology |
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Call number: | SPRINGER-2012-9781461418092:ONLINE Show nearby items on shelf |
Title: | Algebraic Geometry over the Complex Numbers [electronic resource] |
Author(s): |
Donu Arapura |
Date: | 2012 |
Publisher: | Boston, MA : Springer US |
Size: | 1 online resource |
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Note: | This textbook is a strong addition to existing introductory literature on algebraic geometry. The authors treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjectsusing sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and relatedfields. Unique features of this textbook: - Cont ains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developedsomewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. Algebraic Geometry over the Complex Numbers is intended for graduate level courses in algebraic geometry and related fields. Itcan be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory |
Note: | Springer eBooks |
Contents: | Preface |
1. Plane Curves | |
2. Manifolds and Varieties via Sheaves | |
3. More Sheaf Theory | |
4. Sheaf Cohomology | |
5. de Rham Cohomoloy of Manifolds | |
6. Riemann Surfaces | |
7. Simplicial Methods | |
8. The Hodge Theorem for Riemann Manifolds | |
9. Toward Hodge Theory for Complex Manifolds | |
10. Kahler Manifolds | |
11. A Little Algebraic Surface Theory | |
12. Hodge Structures and Homological Methods | |
13. Topology of Families | |
14. The Hard Lefschez Theorem | |
15. Coherent Sheaves | |
16. Computation of Coherent Sheaves | |
17. Computation of some Hodge numbers | |
18. Deformation Invarian | |
ISBN: | 9781461418092 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Topology |
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Call number: | SPRINGER-2012-9781447129813:ONLINE Show nearby items on shelf |
Title: | Partial Differential Equations 1 [electronic resource] : Foundations and Integral Representations |
Author(s): |
Friedrich Sauvigny |
Date: | 2012 |
Edition: | 2nd ed. 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed ongeometric and complex vari able methods involving integral representations. The following topics are treated: integration and differentiation on manifolds foundations of functional analysis Brouwer's mapping degree generalized analytic functions potential theory and spherical h armonics linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior ofCauchys integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate studentsinterested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study |
Note: | Springer eBooks |
Contents: | Differentiation and Integration on Manifolds |
Foundations of Functional Analysis | |
Brouwers Degree of Mapping | |
Generalized Analytic Functions | |
Potential Theory and Spherical Harmonics | |
Linear Partial Differential Equations in Rn | |
ISBN: | 9781447129813 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics |
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Call number: | SPRINGER-2012-9780817682774:ONLINE Show nearby items on shelf |
Title: | Perspectives in Analysis, Geometry, and Topology [electronic resource] : On the Occasion of the 60th Birthday of Oleg Viro |
Author(s): |
Ilia Itenberg Burglind Jricke Mikael Passare |
Date: | 2012 |
Edition: | 1 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | A Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry, and Topology was held at Stockholm University in May 2008. The choice of subjects of the Symposium and present volume was motivated by the work and mathematicalinterests of Oleg Vir o to whom the Symposium and this volume are dedicated. As a professor of Uppsala University, Viro has made invaluable contributions to Swedish research by complementing the country's longstanding tradition inanalysis with his own renowned expertise in geo metry and topology. Consolidating in a single volume a major portion of the recent, impressive encounters among the fields of analysis, geometry, and topology would be too ambitious. Thecollection of papers in this work still should give some sense of the development of the fields and their interactions. The topics presented by leading experts in their respective fields include: algebraic geometry, in particular, realalgebraic geometry, differential geometry, symplectic and contact geometry, complex analy sis, three- and four-dimensional manifolds, and invariants of links. Also included in the book is the opening speech of the Symposium by LennartCarleson on the Unity of Mathematics. Contributors: S. Akbulut K. Baker R. Berman A. Degtyarev J.-P. Demailly T . Ekholm Y. Eliashberg M. Entov J. Etnyre D. Gay G. Henkin I. Itenberg L. Kauffman K. Kaveh M. Khanevsky V. Kharlamov A.Khovanskii C. Manolescu N. Mishachev N. Mok S. Orevkov L. Polterovich P. Py N. Reshetikhin A. Shumakovitch E. Shustin A. Stipsicz C. St roppel B. Webster C. Woodward |
Note: | Springer eBooks |
Contents: | Preface |
1 Selman Akbulut, Exotic structures on smooth 4 | |
manifolds | |
2 Kenneth Baker, John Etnyre, Rational linking and contact geometry | |
3 Robert Berman, Jean | |
Pierre Demailly, Regularity of plurisubharmonic upper envelopes in big cohomology classes | |
4 Alex Degtarev, Towards the generalized Shapiro and Shapiro conjecture | |
5 Alex Degtarev, Ilia Itenberg, Viatcheslav Kharlamov, On the number of components of a complete intersection of real quadrics | |
6 Tobias Ekholm, Rational Symplectic Field Theory and linearized Legendrian contact homology | |
7 Yakov Eliashberg, N. Mishachev, Wrinkling | |
ISBN: | 9780817682774 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v296 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Geometry , Topology |
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Call number: | SPRINGER-2012-9780817646936:ONLINE Show nearby items on shelf |
Title: | An Introduction to Riemann Surfaces [electronic resource] |
Author(s): |
Terrence Napier Mohan Ramachandran |
Date: | 2012 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L -method, a powerful technique used in the theory of several complex variables. The work features a simpleconstruction of a strictly s ubharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such asthe Mittag-Leffler, Weierstrass, and Runge theorem s the RiemannRoch theorem the Serre duality and Hodge decomposition theorems and the uniformization theorem. The book also contains treatments of other facts concerning theholomorphic, smooth, and topological structure of a Riemann surface, such as the bi holomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schnflies theorem (and theJordan curve theorem), and the existence of smooth structures on second countable surfaces. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the onlyprerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercis esmany of which lead to further development of the theoryand presents (with proofs)streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester grad uate course |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Complex analysis in C | |
Riemann Surfaces and the L2 \delta | |
Method for Scalar | |
Valued Forms | |
The L2 \delta | |
Method in a Holomorphic Line Bundle | |
Compact Riemann Surfaces | |
Uniformization and Embedding ofRiemann Surfaces | |
Holomorphic Structures on Topological Surfaces | |
Background Material on Analysis in Rnand Hilbert Space Theory | |
Background Material on Linear Algebra | |
Background Material on Manifolds | |
Background Material on Fundamental Groups, Covering Spaces, and (Co)homology | |
Background Material on Sobolev Spaces and Regularity | |
References | |
Not | |
ISBN: | 9780817646936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Cornerstones |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2012-9780387847948:ONLINE Show nearby items on shelf |
Title: | Structure and Geometry of Lie Groups [electronic resource] |
Author(s): |
Joachim Hilgert Karl-Hermann Neeb |
Date: | 2012 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
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Note: | This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.Building onthe authors' Lie-Gruppen undLie-Algebren textbook from 1991, itp resents the fundamental principles of Lie groupswhile incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometryin the field. The text is entirely self contained,and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretelyand directly illustratethe correspondence between groups and their Lie algebras. In the second part of the book, theauthorsinvestigate the basic structure and representation theory of finite dimensional Lie algebras,suchasthe rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (ro ot decompositions), and questions related to representation theory. In the third part of the book, the authorsturn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, thefourth part of the book deals with th e structure theory of Lie groups, includingsome refined applications of theexponential function, various classes of Lie groups, andstructural issues for general Lie groups. To round out the book's content, several appendices appear at the end of thislast part. Containing a wealth of useful information,including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups andis a valuable addition to the literature. Prerequisites are generally kept to a minimum , and various pedagogicalfeatures make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more adva |
Note: | Springer eBooks |
Contents: | Preface |
1 Introduction | |
Part I Matrix Groups | |
2 Concrete Matrix Groups | |
3The Matrix Exponential Function | |
4Linear Lie Groups | |
Part II Lie Algebras | |
5Elementary Structure Theory of Lie Algebras | |
6Root Decomposition | |
7Representation Theory of Lie Algebras | |
Part III Manifolds and Lie Groups | |
8 Smooth Manifolds | |
9 Basic Lie Theory | |
10 Smooth Actions of Lie Groups | |
Part IV Structure Theory of Lie Groups | |
11 Normal Subgroups, Nilpotemt and Solvable Lie Groups | |
12 Compact Lie Groups | |
13 Semisimple Lie Groups | |
14 General Structure Theory | |
15 Complex Lie | |
ISBN: | 9780387847948 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Global differential geometry , Algebraic topology |
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Call number: | SPRINGER-2011-9783642222504:ONLINE Show nearby items on shelf |
Title: | Stein Manifolds and Holomorphic Mappings [electronic resource] : The Homotopy Principle in Complex Analysis |
Author(s): |
Franc Forstneri |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | None. The Ergebnisse volumes do not have back cover texts |
Note: | Springer eBooks |
ISBN: | 9783642222504 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v56 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functions of complex variables |
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Call number: | SPRINGER-2011-9783642203008:ONLINE Show nearby items on shelf |
Title: | Complex and Differential Geometry [electronic resource] : Conference held at Leibniz Universitt Hannover, September 14 18, 2009 |
Author(s): |
Wolfgang Ebeling Klaus Hulek Knut Smoczyk |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains the Proceedings of the conference Complex and Differential Geometry 2009, held at Leibniz Universitt Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists fromdifferential geometry and (complex ) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in(classical) algebraic geometry through complex geometr y, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology |
Note: | Springer eBooks |
Contents: | Participants |
Surfaces of general type with geometric genus zero: a survey | |
Holomorphic symplectic geometry: a problem list | |
Generalized Lagrangian mean curvature flow in Khler manifolds that are almost Einstein | |
Einstein metrics and preserved curvature conditions for the Ricci flow | |
Differential Harnack Estimates for Parabolic Equations | |
Euler characteristic of a complete intersection | |
Cremona special sets of points in products of projective spaces | |
Stable bundles and polyvector fields | |
Buser | |
Sarnak invariant and projective normality of abelian varieties | |
Complete Kahl | |
ISBN: | 9783642203008 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics, 2190-5614 : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2011-9783642110481:ONLINE Show nearby items on shelf |
Title: | Classi caratteristiche e questioni connesse [electronic resource] |
Author(s): |
E Martinelli |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | I. Bucur:Lanneau de Chow dune varit algbrique.- E. Eckmann: Cohomologie et classes caractristiques.- C. Teleman: Sur le caractre de Chern dun fibr vectoriel complexe diffrentiable.- E. Thomas:Characteristic classes and differentiable manifolds.- A. V an de Ven: Chern classes and complex manifolds |
Note: | Springer eBooks |
Contents: | I. Bucur:Lanneau de Chow dune varit algbrique |
E. Eckmann: Cohomologie et classes caractristiques | |
C. Teleman: Sur le caractre de Chern dun fibr vectoriel complexe diffrentiable | |
E. Thomas: Characteristic classes and differentiable manifolds | |
A. Van de Ven: Chern classes and complex manifolds | |
ISBN: | 9783642110481 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v41 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Global differential geometry |
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Call number: | SPRINGER-2011-9783034800495:ONLINE Show nearby items on shelf |
Title: | Pseudo-Differential Operators: Analysis, Applications and Computations [electronic resource] |
Author(s): |
Luigi Rodino M. W Wong Hongmei Zhu |
Date: | 2011 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London onJuly 1318, 2009. Feature d in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes Advances inPseudo-Differential Operators, Pseudo-Differential Operators and Related Topics, Modern Trends in Pseudo-Differential Operators, New Developments in Pseudo-Differential Operators and Pseudo-DifferentialOperators: Complex Analysis and Partial Differential Equations published in the same series in, respecti vely, 2004, 2006, 2007, 2009 and 2010 |
Note: | Springer eBooks |
Contents: | Preface |
Adaptive Wavelet Computations for Inverses of Pseudo | |
Differential Operators | |
Spectral Theory of Pseudo | |
Differential Operators on S1 | |
A Characterization of Compact Pseudo | |
Differential Operators on S1 | |
Melin Operator with Asymptotics on Manifolds with Corners | |
The Iterative Structure of the Corner Calculus | |
Elliptic Equations and Boundary Value Problems in Non | |
Smooth Domains | |
Calculus of Pseudo | |
Differential Operators and a Local Index of Dirac Operators | |
Lp Bounds for a Class of Fractional Powers of Subelliptic Operators | |
The Heat Kernel and Green Function of the Gener | |
ISBN: | 9783034800495 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v213 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory , Differential equations, partial , Geometry , Computer engineering |
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Call number: | SPRINGER-2011-9781461411055:ONLINE Show nearby items on shelf |
Title: | An Invitation to Morse Theory [electronic resource] |
Author(s): |
Liviu Nicolaescu |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part containsthe foundations of M orse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. Thisis the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations,and will be of interest to graduate students as well as research ers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Some features of thesecond edition include added applications, such as Morse theory and the curvature of knot s, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter onMorse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first editi on |
Note: | Springer eBooks |
Contents: | Preface |
Notations and Conventions | |
1 Morse Functions | |
2 The Topology of Morse Functions | |
3 Applications | |
4 Morse | |
Smale Flows and Whitney Stratifications | |
5 Basics of Complex Morse Theory | |
6 Exercises and Solutions | |
References | |
Index | |
ISBN: | 9781461411055 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2011-9780857296030:ONLINE Show nearby items on shelf |
Title: | Singularities of integrals [electronic resource] : Homology, hyperfunctions and microlocal analysis |
Author(s): |
Frdric Pham |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Bringing together two fundamental texts from Frdric Phams research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Usingnotions developed by J. Leray i n the calculus of residues in several variables and R. Thoms isotopy theorems, Frdric Phams foundational study of the singularities of integrals lies at the interface between analysis andalgebraic geometry, culminating in the Picard-Lefschetz formulae. Th ese mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from thepoint of view of hyperfunction theory and microlocal analysis. Providing a must-have introduc tion to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. Thisbook will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frdr ic Pham, now retired, was Professor at the University of Nice. He has published several educational and researchtexts. His recent work concerns semi-classical analysis and resurgent functions |
Note: | Springer eBooks |
Contents: | Differentiable manifolds |
Homology and cohomology of manifolds | |
Lerays theory of residues | |
Thoms isotopy theorem | |
Ramification around Landau varieties | |
Analyticity of an integral depending on a parameter | |
Ramification of an integral whose integrand is itself ramified | |
Functions of a complex variable in the Nilsson class | |
Functions in the Nilsson class on a complex analytic manifold | |
Analyticity of integrals depending on parameters | |
Sketch of a proof of Nilssons theorem | |
Examples: how to analyze integrals with singular integrands | |
Hyperfunctions in one variable, | |
ISBN: | 9780857296030 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Differential equations, partial |
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Call number: | SPRINGER-2011-9780857290304:ONLINE Show nearby items on shelf |
Title: | Holomorphic Function Theory in Several Variables [electronic resource] : An Introduction |
Author(s): |
Christine Laurent-Thibaut |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques toseveral variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Threeappendices on differential manifolds, sheaf theory a nd functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. Newconcepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchersseeking an introduction to holomorphic function theory in several variables and lecturers seeking a conci se book on the subject |
Note: | Springer eBooks |
Contents: | Elementary local properties of holomorphic functions of several complex variables |
Currents and complex structures | |
The Bochner | |
Martinelli | |
Koppelman kernel and formula applications | |
Extensions of CR functions | |
Extensions of holomorphic and CR functions on manifolds | |
Domains of holomorphy and pseudoconvexity | |
The Levi problem and the resolution of in strictly pseudoconvex domains | |
Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary | |
Appendices | |
ISBN: | 9780857290304 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2011-9780817682477:ONLINE Show nearby items on shelf |
Title: | The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator [electronic resource] |
Author(s): |
J. J Duistermaat |
Date: | 2011 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Khler casethe Dolbeault operator is no longer suitable for getting local formulas for theRiemannRoch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heatkernels theory of Berline, Getzler, and Vergne,this workrevis its some fundamental concepts of the theory, and presents the application to symplectic geometry. J.J. Duistermaat was well known for his beautiful and conciseexpositions of seemingly familiar concepts, and this classic studyis certainly no exception. Rep rinted as it was originally published,this workis as an affordable textthat will be of interest to a range of researchers ingeometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject. Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[tothe]spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. EMS Newsletter The author's book is a marvelous introduction to [these] objects andtheories. Zentralblatt MATH |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 The Dolbeault | |
Dirac Operator | |
3 Clifford Modules | |
4 The Spin Group and the Spin | |
c Group | |
5 The Spin | |
c Dirac Operator | |
6 Its Square | |
7 The Heat Kernel Method | |
8 The Heat Kernel Expansion | |
9 The Heat Kernel on a Principal Bundle | |
10 The Automorphism | |
11 The Hirzebruch | |
Riemann | |
Roch Integrand | |
12 The Local Lefschetz Fixed Point Formula | |
13 Characteristic Case | |
14 The Orbifold Version | |
15 Application to Symplectic Geometry | |
16 Appendix: Equivariant Forms | |
ISBN: | 9780817682477 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis , Operator theory , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2010-9783642120558:ONLINE Show nearby items on shelf |
Title: | Shapes and Diffeomorphisms [electronic resource] |
Author(s): |
Laurent Younes |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Shapes are complex objects, which are difficult to apprehend as mathematical entities, in ways that can also be amenable to computerized analysis and interpretation. This volume provides the background that is required for thispurpose, including diff erent approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act onthem, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections thatrepresent the state of the art in the analysis of shapes and their defor mations. A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy |
Note: | Springer eBooks |
Contents: | Introduction |
1. Parametrized Plane Curves | |
2. Medial Axis | |
3. Moment | |
Based Representation | |
4. Local Properties of Surfaces | |
5. Isocontours and Isosurfaces | |
6. Evolving Curves and Surfaces | |
7. Deformable templates | |
8. Ordinary Differential Equations and Groups of Diffeomorphisms | |
9. Building Admissible Spaces | |
10. Deformable Objects and Matching Functionals | |
11. Diffeomorphic Matching | |
12. Distances and Group Actions | |
13. Metamorphosis | |
A. Elements from Hilbert Space Theory | |
B. Elements from Differential Geometry | |
C. Ordinary Differential Equations | |
D. Optimiz | |
ISBN: | 9783642120558 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Applied Mathematical Sciences, 0066-5452 : v171 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Visualization , Global differential geometry |
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Call number: | SPRINGER-2010-9781441908988:ONLINE Show nearby items on shelf |
Title: | Operational Spacetime [electronic resource] : Interactions and Particles |
Author(s): |
Heinrich Saller |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Operational Spacetime: Interactions and Particles provides readers with a basic understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for theparametrization of op eration Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physicalproperties are related eigenvalues or invarian ts. As an explicit example, an operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge-isospin group in the general lineargroup in two complex dimensions, i.e., the Lorentz cover group, extend ed by the causal (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically,with the properties of interactions and particles as arising in the representations of its tan gent Minkowski spaces. Heinrich Saller is the author of Operational Quantum Theory I: Nonrelativistic Structures (Springer, 2006) andOperational Quantum Theory II: Relativistic Structures (Springer, 2006) |
Note: | Springer eBooks |
Contents: | Introduction and Orientation |
Einstein's Gravity | |
Riemannian Manifolds | |
Mass Points | |
Quantum Mechanics | |
Quantum Fields of Flat Spacetime | |
External and Internal Operations | |
Relativities and Homogeneous Spaces | |
Representation Coefficients | |
Convolutions and Product Representations | |
Interactions and Kernels | |
Electroweak Spacetime | |
Masses and Coupling Constants | |
ISBN: | 9781441908988 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Fundamental Theories of Physics : v163 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2010-9781441904348:ONLINE Show nearby items on shelf |
Title: | CR Submanifolds of Complex Projective Space [electronic resource] |
Author(s): |
Mirjana Djoric Masafumi Okumura |
Date: | 2010 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader totopics of current research and to more advanced publications. The book begins with an introduction to the geometry of complex manifolds and their submanifolds and describes the properties of hypersurfaces and CR submanifolds, withparticular emphasis on CR submanifolds of maximal CR dimension. The second part contains results which are not new, but recently published in some mathematical journals. The final part contains several original results by the authors,with complete proofs. Key features of CR Submanifolds of Complex Projecti ve Space: - Presents recent developments and results in the study of submanifolds previously published only in research papers. - Special topics exploredinclude: the Khler manifold, submersion and immersion, codimension reduction of a submanifold, tubes o ver submanifolds, geometry of hypersurfaces and CR submanifolds of maximal CR dimension. - Provides relevant techniques, resultsand their applications, and presents insight into the motivations and ideas behind the theory. - Presents the fundamental defin itions and results necessary for reaching the frontiers of research in this field. This text is largelyself-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced under graduates, graduate students and researchers in differential geometry will benefitfrom this concise approach to an important topic |
Note: | Springer eBooks |
Contents: | 1. Complex manifold |
2. Almost complex structure | |
3. Complex vector space complexification | |
4. Khler manifold | |
5. Structure equations of a submanifold | |
6. Submanifolds of a Euclidean space | |
7. Submanifolds of a complex manifold | |
8. The Levi form | |
9. The principal circle bundle S^{2n+1}({\bf P}^n({\bf C}),S^1) | |
10. Submersion and immersion | |
11. Hypersurfaces of a Riemannian manifold of constant curvature | |
12. Hypersurfaces of a sphere S^{n+1}(1/a) | |
13. Hypersurfaces of a sphere with parallel shape operator | |
14. Codimension reduction of a submanifold | |
15. CR submani | |
ISBN: | 9781441904348 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt, 1389-2177 : v19 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2010-9780817649593:ONLINE Show nearby items on shelf |
Title: | Riemannian Geometry of Contact and Symplectic Manifolds [electronic resource] |
Author(s): |
David E Blair |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides manyillustrative examples for the reader. Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics includea complex geodesic flow and the accompanying g eometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of tienneGhys's attractive notion of a holomorphic Anosov flow. Researchers, m athematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemanniangeometry is a prerequisite. Reviews from the First Edition: The book . . . can be used eithe r as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the mainideas . . . and studies a vast amount of related subjects such as integral sub-manifolds, symplectic structure of t angent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics.Mathematical Reviews this is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive[table of] contents and useful ideas for pursuing their studies. Memoriile Sectiilor Stiintifice |
Note: | Springer eBooks |
Contents: | Preface |
1. Symplectic Manifolds | |
2. Principal bundles | |
3. Contact Manifolds | |
4. Associated Metrics | |
5. Integral Submanifolds and Contact Transformations | |
6. Sasakian and Cosymplectic Manifolds | |
7. Curvature of Contact Metric Manifolds | |
8. Submanifolds of Khler and Sasakian Manifolds | |
9. Tangent Bundles and Tangent Sphere Bundles | |
10. Curvature Functionals and Spaces of Associated Metrics | |
11. Negative Xi | |
sectional Curvature | |
12. Complex Contact Manifolds | |
13. Additional Topics in Complex Geometry | |
14. 3 | |
Sasakian Manifolds | |
Bibliography | |
Subjec | |
ISBN: | 9780817649593 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v203 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global differential geometry , Cell aggregation Mathematics |
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Call number: | SPRINGER-2010-9780817649135:ONLINE Show nearby items on shelf |
Title: | Hyperbolic Manifolds and Discrete Groups [electronic resource] |
Author(s): |
Michael Kapovich |
Date: | 2010 |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is onThurstons hyperbolization t heorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to thehyperbolization theorem as well as rich discussions on related t opics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich setof examples, numerous exercises, and an extensive bibliography and index, Hyperbolic M anifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairlyself-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem,this is an important book which had to be written some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolizationtheorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. -- -Zentralbatt MATH This book can act as source material for a postgraduatecourse and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide |
Note: | Springer eBooks |
Contents: | Preface |
Three | |
dimensional Topology | |
Thurston Norm | |
Geometry of the Hyperbolic Space | |
Kleinian Groups | |
Teichmller Theory of Riemann Surfaces | |
Introduction to the Orbifold Theory | |
Complex Projective Structures | |
Sociology of Kleinian Groups | |
Ultralimits of Metric Spaces | |
Introduction to Group Actions on Trees | |
Laminations, Foliations and Trees | |
Rips Theory | |
Brooks' Theorem and Circle Packings | |
Pleated Surfaces and Ends of Hyperbolic Manifolds | |
Outline of the Proof of the Hyperbolization Theorem | |
Reduction to The Bounded Image Theorem | |
The Bounded Image Theorem | |
ISBN: | 9780817649135 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Geometry , Topology , Cell aggregation Mathematics |
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Call number: | SPRINGER-2009-9783642006395:ONLINE Show nearby items on shelf |
Title: | Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication [electronic resource] |
Author(s): |
Christian Rohde |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods. Firstly, the methodof E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers andinvolutions are obtained. Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized.Moreover fibers with complex multiplication of these new families are also dete rmined. This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties withcomplex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line arecomputed for a broad range of examples |
Note: | Springer eBooks |
Contents: | 1 An introduction to Hodge structures and Shimura varieties |
2 Cyclic covers of the projective line | |
3 Some preliminaries for families of cyclic covers | |
4 The Galois group decomposition of the Hodge structure | |
5 The computation of the Hodge group | |
6 Examples of families with dense sets of complex multiplication fibers | |
7 The construction of Calabi | |
Yau manifolds with complex multiplication | |
8 The degree 3 case | |
9 Other examples and variations | |
10 Examples of CMCY families of 3 | |
manifolds and their invariants | |
11 Maximal families of CMCY type | |
ISBN: | 9783642006395 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1975 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic |
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Call number: | SPRINGER-2009-9783540886068:ONLINE Show nearby items on shelf |
Title: | Topology-Based Methods in Visualization II [electronic resource] |
Author(s): |
Hans-Christian Hege Konrad Polthier Gerik Scheuermann |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Visualization research aims at providing insights into large, complex bodies of data. Topological methods are distinguished by their solid mathematical foundation, guiding the algorithmic analysis and its presentation among thevarious visualization t echniques. This book contains 13 peer-reviewed papers resulting from the second workshop on Topology-Based Methods in Visualization, held 2007 in Grimma near Leipzig, Germany. All articles present original,unpublished work from leading experts. Together, these articles present the state of the art of topology-based visualization research |
Note: | Springer eBooks |
Contents: | Visualization of Coherent Structures in Transient 2D Flows: C.Garth et al |
Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology: F. Sadlo et al | |
Extraction of Separation Manifolds using Topological Structures in Flow Cross Sections: A. Wiebel et al | |
Topology Based Selection and Curation of Level Sets: C.Bajaj et al | |
Representing Interpolant Topology for Contour Tree Computation: H. Carr et al | |
Path Line Attributes | |
an Information Visualization Approach to Analyzing the Dynamic Behavior of 3D Time | |
Dependent Flow Fields: K. Shi et al | |
Flow Structure based | |
ISBN: | 9783540886068 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Visualization, 1612-3786 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer graphics , Visualization , Geometry , Topology , Engineering , Mechanical engineering |
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Call number: | SPRINGER-2008-9783764374785:ONLINE Show nearby items on shelf |
Title: | Analysis II [electronic resource] |
Author(s): |
Herbert Amann Joachim Escher |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and cleardevelopment that started in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is representedin traditional textbooks. This applies, for ins tance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. Another exampleis the presentation of the local theory of submanifolds of Rn |
Note: | Springer eBooks |
Contents: | Preface |
VI. Integral Calculus in One Variable | |
1. Step Continuous Functions | |
2. Continuous Extensions | |
3. The Cauchy | |
Riemann Integral | |
4. Properties of the Integral | |
5. The Technology of Integration | |
6. Sums and Integrals | |
7. Fourier Series | |
8. Improper Integrals | |
9. The Gamma Function | |
VII. Differential Calculus in Several Variables | |
1. Continuous Linear Mappings | |
2. Differentiability | |
3. Calculation Rules | |
4. Multilinear Mappings | |
5. Higher Derivatives | |
6. Nemytski Operators and Calculus of Variations | |
7. Inverse Mappings | |
8. Implicit Functions | |
9. Manifolds | |
10. Tang | |
ISBN: | 9783764374785 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis , Functions of complex variables , Functions, special |
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Call number: | SPRINGER-2008-9783540737506:ONLINE Show nearby items on shelf |
Title: | Principal Manifolds for Data Visualization and Dimension Reduction [electronic resource] |
Author(s): |
Alexander N Gorban Balzs Kgl Donald C Wunsch Andrei Y Zinovyev |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA),Multidimensional Scaling (MDS) , Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding andclustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described as well. Presentation of algorithms is supplemented by casestudies, from engineering to astronomy, but mostly of biological data: a nalysis of microarray and metabolite data. The volume ends with a tutorial PCA and K-means decipher genome. The book is meant to be useful for practitioners inapplied data analysis in life sciences, engineering, physics and chemistry it will also be valua ble to PhD students and researchers in computer sciences, applied mathematics and statistics |
Note: | Springer eBooks |
Contents: | Developments and Applications of Nonlinear Principal Component Analysis a Review |
Nonlinear Principal Component Analysis: Neural Network Models and Applications | |
Learning Nonlinear Principal Manifolds by Self | |
Organising Maps | |
Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization | |
Topology | |
Preserving Mappings for Data Visualisation | |
The Iterative Extraction Approach to Clustering | |
Representing Complex Data Using Localized Principal Components with Application to Astronomical Data | |
Auto | |
Associative Models, Nonlinear P | |
ISBN: | 9783540737506 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Computational Science and Enginee, 1439-7358 : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Mathematical physics , Mathematical statistics , Engineering |
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Call number: | SPRINGER-2008-9781848000544:ONLINE Show nearby items on shelf |
Title: | Isomonodromic Deformations and Frobenius Manifolds [electronic resource] : An Introduction |
Author(s): |
Claude Sabbah |
Date: | 2008 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of thetheory has opened new per spectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometricmethods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recentresearch questions related to mirror symmetry. The fundamental tool used within the book is that of a vector bundle with connection. There is a detailed analysis of the singularities of such objects and of their deformations, andcoverage of the techniques used in the resolution of the Riemann-Hilbert problem and Birkhoffs pro blem. An approach to Frobenius manifolds using isomonodromic deformations of linear differential equations is also developed. Aimed atgraduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry |
Note: | Springer eBooks |
Contents: | The language of fibre bundles |
Holomorphic vector bundles on the Riemann sphere | |
The Riemann | |
Hilbert correspondence on a Riemann surface | |
Lattices | |
The Riemann | |
Hilbert problem and Birkhoffs problem | |
Fourier | |
Laplace duality | |
Integrable deformations of bundles with connection on the Riemann sphere | |
Saito structures and Frobenius structures on a complex analytic manifold | |
ISBN: | 9781848000544 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic |
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Call number: | SPRINGER-2008-9780817646431:ONLINE Show nearby items on shelf |
Title: | Conformal Groups in Geometry and Spin Structures [electronic resource] |
Author(s): |
Pierre Angls |
Date: | 2008 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Conformal groups play a key role in geometry and spin structures. This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley andprogressing to recent re search in spinors and conformal geometry. Key topics and features: * Focuses initially on the basics of Clifford algebras * Studies the spaces of spinors for some even Clifford algebras * Examines conformal spingeometry, beginning with an elementary study of the conformal group of the Euclidean plane * Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group *Introduces conformal flat geometry and conformal spinoriality groups, f ollowed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Discusses links between classical spinstructures and conformal spin structures in the context of conformal connections * Examines pseudo-u nitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classicalpseudo-unitary space * Ample exercises with many hints for solutions * Comprehensive bibliography and index This text is suitable f or a course in mathematical physics at the advanced undergraduate and graduate levels. It will alsobenefit researchers as a reference text |
Note: | Springer eBooks |
Contents: | Classic Groups: Clifford Algebras, Projective Quadrics, and Spin Groups |
Real Conformal Spin Structures | |
Pseudounitary Conformal Spin Structures | |
ISBN: | 9780817646431 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematical Physics : v50 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Matrix theory , Geometry , Number theory , Mathematical physics |
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Call number: | SPRINGER-2008-9780387738925:ONLINE Show nearby items on shelf |
Title: | Differential Analysis on Complex Manifolds [electronic resource] |
Author(s): |
Raymond O Wells |
Date: | 2008 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds withvector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds,differential operators on a Kahler manifold, th e Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira'svanishing and embedding theorems. The third edition of this standard r eference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared.From reviews of the 2nd Edition: ..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work. - NigelHitchin, Bulletin of the London Mathematical Society Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material. - Daniel M. Burns, Jr.,Mathematical Reviews |
Note: | Springer eBooks |
Contents: | Manifolds and Vector Bundles |
Sheaf Theory | |
Differential Geometry | |
Elliptic Operator Theory | |
Compact Complex Manifolds | |
Kodaira's Projective Embedding Theorem | |
ISBN: | 9780387738925 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v65 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Global analysis |
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Call number: | SPRINGER-2007-9783764383503:ONLINE Show nearby items on shelf |
Title: | Labyrinth of Thought [electronic resource] : A History of Set Theory and Its Role in Modern Mathematics |
Author(s): |
Jos Ferreirs |
Date: | 2007 |
Edition: | Second revised edition |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of Georg Cantor, it analyzes hiswork and the emergence of transfinite set theory within the broader context of the rise of modern mathematics. The text has a tripartite structure. Part 1, The Emergence of Sets within Mathematics, surveys the initial motivations for amathematical notion of a set within several b ranches of the discipline (geometry, algebra, algebraic number theory, real and complex analysis), emphasizing the role played by Riemann in fostering acceptance of the set-theoreticapproach. In Part 2, Entering the Labyrinth, attention turns to the earli est theories of sets, their evolution, and their reception by the mathematical community prominent are the epoch-making contributions of Cantor and Dedekind, andthe complex interactions between them. Part 3, In Search of an Axiom System, studies the four- decade period from the discovery of set-theoretic paradoxes to Gdels independence results, an era during which set theory graduallybecame assimilated into mainstream mathematics particular attention is given to the interactions between axiomatic set theor y and modern systems of formal logic, especially the interplay between set theory and type theory. A newEpilogue for this second edition offers further reflections on the foundations of set theory, including the dichotomy conception and the well-known ite rative conception. The author paints on a grand scale. He sees clearly, and hesees whole. The result is a spacious canvas full of intriguing scenes and portraits from the history of set theory, seamlessly juxtaposed to form a fascinating and accurate pict ure of a vast area of modern mathematics. It is amust-have book for anyone who wishes to gain a balanced picture of this history. It is written in clear and elegant language for the learner, w |
Note: | Springer eBooks |
Contents: | The Emergence of Sets within Mathematics |
Institutional and Intellectual Contexts in German Mathematics, 18001870 | |
A New Fundamental Notion: Riemanns Manifolds | |
Dedekind and the Set | |
theoretical Approach to Algebra | |
The Real Number System | |
Origins of the Theory of Point | |
Sets | |
Entering the Labyrinth | |
Toward Abstract Set Theory | |
The Notion of Cardinality and the Continuum Hypothesis | |
Sets and Maps as a Foundation for Mathematics | |
The Transfinite Ordinals and Cantors Mature Theory | |
In Search of an Axiom System | |
Diffusion, Crisis, and Bifurcation: 1890 to 1914 | |
Logic | |
ISBN: | 9783764383503 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematics_$xHistory |
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Call number: | SPRINGER-2007-9783764381158:ONLINE Show nearby items on shelf |
Title: | Holomorphic Morse Inequalities and Bergman Kernels [electronic resource] |
Author(s): |
Xiaonan Ma George Marinescu |
Date: | 2007 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book gives for the first time a self-contained and unified approach to holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel, and presents also variousapplications. The main analy tic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several activeareas of research in complex, Khler and symplectic g eometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, acompactification of complete Khler manifolds of pinched negative curvature , the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion |
Note: | Springer eBooks |
Contents: | 0. Introduction |
1. Demailly's Holomorphic Morse Inequalities | |
2. Characterization of Moishezon Manifolds | |
3. Holomorphic Morse Inequalities on Non | |
compact Manifolds | |
4. Asymptotic Expansion of the Bergman Kernel | |
5. Kodaira Map | |
6. Bergman Kernel on Non | |
compact Manifolds | |
7. Toeplitz Operators | |
8. Bergman Kernels on Symplectic Manifolds | |
Appendix | |
A. Sobolev Spaces | |
B. Elements of Analytic and Hermitian Geometry | |
C. Spectral Analysis of Self | |
adjoint Operators | |
D. Heat Kernel and Finite Propagation Speed | |
E. Harmonic Oscillator | |
ISBN: | 9783764381158 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v254 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Differential equations, partial , Global differential geometry |
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Call number: | SPRINGER-2007-9783540691532:ONLINE Show nearby items on shelf |
Title: | Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds [electronic resource] |
Author(s): |
Alexander Isaev |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds withhigh-dimensional gro ups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensivelystudied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds |
Note: | Springer eBooks |
Contents: | The Homogeneous Case |
The Case d(M) = n2 | |
The Case d(M) = n2 | |
1, n ? 3 | |
The Case of (2,3) | |
Manifolds | |
Proper Actions | |
ISBN: | 9783540691532 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1902 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2007-9780387495101:ONLINE Show nearby items on shelf |
Title: | An Invitation to Morse Theory [electronic resource] |
Author(s): |
Liviu Nicolaescu |
Date: | 2007 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part containsthe foundations of M orse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetztheory. This is the first textbook to inc lude topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations,and will be of interest to graduate students as well as research ers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Liviu Nicolaescu isAssociate Professor of Mathematics at University of Notre Dame |
Note: | Springer eBooks |
Contents: | Preface |
Notations and conventions | |
Morse functions | |
The topology of Morse functions | |
Applications | |
Basics of complex Morse theory | |
Exercises and solutions | |
References | |
Index | |
ISBN: | 9780387495101 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis , Cell aggregation Mathematics |
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Call number: | SPRINGER-2006-9783764375362:ONLINE Show nearby items on shelf |
Title: | The Monodromy Group [electronic resource] |
Author(s): |
Henryk odek |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures.In the theory of syste ms of linear differential equations one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliationsthere appear the Ecalle-Voronin-Martinet-Ram is moduli. On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. All this is presented in this book,underlining the unifying role of the monodromy group. The material is add ressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. The book contains a lot of resultswhich are usually spread in many sources. Readers can quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galoistheory, and parts of algebraic geometry, without searching in vast literature |
Note: | Springer eBooks |
Contents: | Analytic Functions and Morse Theory |
Normal Forms of Functions | |
Algebraic Topology of Manifolds | |
Topology and Monodromy of Functions | |
Integrals along Vanishing Cycles | |
Vector Fields and Abelian Integrals | |
Hodge Structures and Period Map | |
Linear Differential Systems | |
Holomorphic Foliations. Local Theory | |
Holomorphic Foliations. Global Aspects | |
The Galois Theory | |
Hypergeometric Functions | |
ISBN: | 9783764375362 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Monografie Matematyczne : v67 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functions of complex variables , Differential Equations , Functions, special , Algebraic topology |
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Call number: | SPRINGER-2006-9783764373955:ONLINE Show nearby items on shelf |
Title: | On the Topology of Isolated Singularities in Analytic Spaces [electronic resource] |
Author(s): |
Jos Seade |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostlydevoted to complex sing ularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor the relation with3-dimensional Lie groups exotic spheres spin st ructures and 3-manifold invariants the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part ofthe book studies pioneer work about real analytic singularities which ari se from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred linksin the 3-sphere defined by meromorphic functions. This provides new methods for constructing m anifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematiciansand researchers interested in geometry and topology |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
A Fast Trip through the Classical Theory | |
Motions in Plane Geometry and the 3 | |
Dimensional Brieskorn Manifolds | |
3 | |
Dimensional Lie Groups and Surface Singularities | |
Within the Realm of the General Index Theorem | |
On the Geometry and Topology of Quadrics in CP^n | |
Real Singularities and Complex Geometry | |
Real Singularities with a Milnor Fibration | |
Real Singularities and Open Book Decompositions of the 3 | |
Sphere | |
Bibliography | |
Index | |
ISBN: | 9783764373955 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v241 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functions of complex variables , Global differential geometry , Algebraic topology |
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Call number: | SPRINGER-2006-9783540344599:ONLINE Show nearby items on shelf |
Title: | Partial Differential Equations 1 [electronic resource] : Foundations and Integral Representations |
Author(s): |
Friedrich Sauvigny |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEsand complex variable m ethods. In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potentialtheory and spherical harmonics, Linear part ial differential equations. While we solve the partial differential equations via integral representations in this volume, we shall present functional analytic solution methods in the secondvolume. This textbook can be chosen for a course over several sem esters on a medium level. Advanced readers may study each chapter independently from the others |
Note: | Springer eBooks |
Contents: | Differentiation and Integration on Manifolds |
Foudations of Functional Analysis | |
Brouwers Degree of Mapping with Geometric Applications | |
Generalized Analytic Functions | |
Potential Theory and Spherical Harmonics | |
Linear Partial Differential Equations in Rn | |
ISBN: | 9783540344599 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Mathematical physics |
Availability: | Click here to see Library holdings or inquire at
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More info: | Amazon.com |
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Location: | ONLINE |
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