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SPIRES-BOOKS: FIND KEYWORD ALGEBRAIC TOPOLOGY *END*INIT* use /tmp/qspiwww.webspi1/20836.66 QRY 131.225.70.96 . find keyword algebraic topology ( in books using www Cover
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Call number:9783319461434:ONLINE Show nearby items on shelf
Title:The Universal Coefficient Theorem and Quantum Field Theory A Topological Guide for the Duality Seeker
Author(s): Andrei-Tudor Patrascu
Date:2017
Size:1 online resource (XVI, 270 p. 6 illus., 1 illus. in color p.)
Contents:Introduction -- Elements of General Topology -- Algebraic Topology -- Homological Algebra -- Connections: Topology and Analysis -- The Atyiah Singer Index Theorem -- Universal Coefficient Theorems -- BV and BRST Quantization, Quantum
Observables and Symmetry -- Universal Coefficient Theorem and Quantum Field Theory -- The Universal Coefficient Theorem and Black Holes -- From Grothendieck’s Schemes to QCD -- Conclusions.
ISBN:9783319461434
Series:eBooks
Series:Springer eBooks
Series:Springer 2017 package
Keywords: Physics , Mathematical physics , Algebraic topology , Quantum field theory , String theory , Elementary particles (Physics) , Physics , Quantum Field Theories, String Theory , Algebraic Topology , Mathematical Applications in the Physical Sciences , Elementary Particles, Quantum Field Theory
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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-2016-9783662493618: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-2016-9783658106331:ONLINE Show nearby items on shelf
Title:Manifolds, Sheaves, and Cohomology
Author(s): Torsten Wedhorn
Date:2016
Size:1 online resource (354 p.)
Note:10.1007/978-3-658-10633-1
Contents:Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis
ISBN:9783658106331
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds
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Call number:SPRINGER-2016-9783319335728:ONLINE Show nearby items on shelf
Title:Open Problems in the Geometry and Analysis of Banach Spaces
Author(s): Antonio J Guirao
Date:2016
Size:1 online resource (169 p.)
Note:10.1007/978-3-319-33572-8
Contents:Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index.
ISBN:9783319335728
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Approximation theory , Functional analysis , Measure theory , Convex geometry , Discrete geometry , Algebraic topology , Mathematics , Functional Analysis , Approximations and Expansions , Measure and Integration , Convex and Discrete Geometry , Algebraic Topology
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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-2016-9783319297880:ONLINE Show nearby items on shelf
Title:Ordered Sets An Introduction with Connections from Combinatorics to Topology
Author(s): Bernd Schröder
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (10 p.)
Note:10.1007/978-3-319-29788-0
Contents:Preface -- Basics -- Chains, Antichains, and Fences -- Upper and Lower Bounds -- Retractions -- Constraint Satisfaction Problems -- Graphs and Homomorphisms -- Lexicographic Sums -- Lattices -- Truncated Lattices -- Dimension -- Interval Orders -- Sets P^Q = Hom (Q, P) and Products -- Enumeration of Ordered Sets -- Appendix A: Some Algebraic Topology -- Appendix B: Some Discrete Morse Theory -- References -- Index
ISBN:9783319297880
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Algebra , Ordered algebraic structures , Mathematical logic , Algebraic topology , Combinatorics , Mathematics , Mathematical Logic and Foundations , Order, Lattices, Ordered Algebraic Structures , Combinatorics , Algebraic Topology
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Call number:SPRINGER-2016-9783319234885:ONLINE Show nearby items on shelf
Title:Homotopical Topology
Author(s): Anatoly Fomenko
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (627 p.)
Note:10.1007/978-3-319-23488-5
Contents:Introduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories
ISBN:9783319234885
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 273
Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , K-theory , Algebraic topology , Mathematics , Category Theory, Homological Algebra , K-Theory , Algebraic Topology
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Call number:SPRINGER-2014-9788847056626:ONLINE Show nearby items on shelf
Title:Topologia [electronic resource]
Author(s): Marco Manetti
Date:2014
Edition:2a edizione
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Nato dall'esperienza dell'autore nell'insegnamento della topologia agli studenti del corso di Laurea in Matematica, questo libro contiene le nozioni fondamentali di topologia generale ed una introduzione alla topologia algebrica.La scelta degli argom enti, il loro ordine di presentazione e, soprattutto, il tipo di esposizione tiene conto delle tendenze attuali nell'insegnamento della topologia e delle novit nella struttura dei corsi di Laurea scientificiconseguenti all'introduzione del sistema 3+2. Qu esta seconda edizione, oltre a semplificare alcune dimostrazioni, presenta una sostanziale riscrittura della parte sui rivestimenti e l'aggiunta di ulteriori esempi il numero complessivodi esercizi proposti stato portato a 500 ed il numero di quelli svol ti a 120
Contents:1 Introduzione geometrica alla topologia
2 Insiemi
3 Strutture topologiche
4 Connessione e compattezza
5 Quozienti topologici
6 Successioni
7 Variet, prodotti infiniti e paracompattezza
8 Complementi di topologia generale
9 Intermezzo
10 Omotopia
11 Il gruppo fondamentale
12 Rivestimenti
13 Monodromia
14 Il teorema di Van Kampen
15 Complementi di topologia algebrica
16 Suggerimenti e soluzioni di alcuni esercizi
ISBN:9788847056626
Series:eBooks
Series:SpringerLink
Series:UNITEXT, 2038-5714 : v78
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology
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Call number:SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf
Title:Basic Modern Algebra with Applications [electronic resource]
Author(s): Mahima Ranjan Adhikari
Avishek Adhikari
Date:2014
Publisher:New Delhi : Springer India : Imprint: Springer
Size:1 online resource
Note:The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource
Contents:Prerequisites: Basics of Set Theory and Integers
Groups: Introductory Concepts
Actions of Groups, Topological Groups and semigroups
Rings: Introductory Concepts
Ideals of Rings: Introductory concepts
Factorization in Integral Domains and in Polynomial Rings
Rings with Chain Conditions
Vector Spaces
Modules
Algebraic Aspects of Number Theory
Algebraic Numbers
Introduction to Mathematical Cryptography
Appendix A: Some Aspects of Semirings
Appendix B: Category Theory
Appendix C: A Brief Historical Note
ISBN:9788132215998
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Number theory
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Call number:SPRINGER-2014-9783642310317:ONLINE Show nearby items on shelf
Title:Vladimir I. Arnold - Collected Works [electronic resource] : Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972
Author(s): Vladimir I Arnold
Alexander B Givental
Boris A Khesin
Alexander N Varchenko
Victor A Vassiliev
Oleg Ya Viro
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. Thissecond volume of his Coll ected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry
Contents:1 Variational principle for three
dimensional steady
state flows of an ideal fluid
2 On the Riemann curvature of diffeomorphism groups
3 Sur la topologie des coulements stationnaires des fluides parfaits (in French)
4 Conditions for non
linear stability of stationary plane curvilinear flows of an ideal fluid
5 On the topology of three
dimensional steady flows of an ideal fluid
6 On an a priori estimate in the theory of hydrodynamical stability
7 On the differential geometry of infinite
dimensional Lie groups and its application to the hydrodynamics of perfect fluids
8 On
ISBN:9783642310317
Series:eBooks
Series:SpringerLink
Series:Vladimir I. Arnold - Collected Works : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Mathematical physics
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Call number:SPRINGER-2014-9783319096803:ONLINE Show nearby items on shelf
Title:Topology [electronic resource] : An Introduction
Author(s): Stefan Waldmann
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and isalso omnipresent in m ore applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on generaltopology, most of them are too large for a fir st bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course
Contents:Introduction
Topological Spaces and Continuity
Construction of Topological Spaces
Convergence in Topological Spaces
Compactness
Continuous Functions
Baires Theorem
ISBN:9783319096803
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology
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Call number:SPRINGER-2014-9783319070346:ONLINE Show nearby items on shelf
Title:Differential Characters [electronic resource]
Author(s): Christian Br
Christian Becker
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the productstructure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.
Contents:Differential Characters and Geometric Chains
Relative differential Cohomology
Index
ISBN:9783319070346
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2112
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global differential geometry , Algebraic topology
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Call number:SPRINGER-2014-9783319067438:ONLINE Show nearby items on shelf
Title:Duality Theories for Boolean Algebras with Operators [electronic resource]
Author(s): Steven Givant
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:In this new text, Steven Givantthe author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarskidevelops three theories of duality for Boolean algebras with operators. Givant addressesthe two most recognized dualit ies (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fieldsof mathematics, computer science, logic, and philos ophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras,as well as the fundamentals of point-set topology
Contents:1. Algebraic Duality
2. Topological Duality
3. Hybrid Duality
ISBN:9783319067438
Series:eBooks
Series:SpringerLink
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Logic, Symbolic and mathematical
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Call number:SPRINGER-2014-9783319064772:ONLINE Show nearby items on shelf
Title:Finiteness Properties of Arithmetic Groups Acting on Twin Buildings [electronic resource]
Author(s): Stefan Witzel
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains onlytwo places. While th e proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory oftwin buildings
Contents:Basic Definitions and Properties
Finiteness Properties of G(Fq[t])
Finiteness Properties of G(Fq[t t
1])
Affine Kac
Moody Groups
Adding Places
ISBN:9783319064772
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Mathematics, 0075-8434 : v2109
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Group theory , Geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2014-9783319056487:ONLINE Show nearby items on shelf
Title:Spectral Mapping Theorems [electronic resource] : A Bluffer's Guide
Author(s): Robin Harte
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several andmany variables. The basic algebraic systems semigroups, rings and linear algebras are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. SpectralMapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory
Contents:Algebra
Topology
Topological algebra
Spectral theory
Several variables
Many Variables
ISBN:9783319056487
Series:eBooks
Series:SpringerLink
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2014-9783319045641:ONLINE Show nearby items on shelf
Title:Towards the Mathematics of Quantum Field Theory [electronic resource]
Author(s): Frdric Paugam
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of themathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primarytarget. This reference work provides a coheren t and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The firstpart of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory ofnon-linear partial differential equations, with applications to general gauge theories. The s econd part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the thirdpart provides an introduction to quantum field theory, presents various renormalization methods, and discusses the q uantization of factorization algebras. The book is primarily intended for pure mathematicians (and in particulargraduate students) who would like to learn about the mathematics of quantum field theory
Contents:Introduction
Mathematical Preliminaries
Classical Trajectories and Fields
Quantum Trajectories and Fields
Appendices
ISBN:9783319045641
Series:eBooks
Series:SpringerLink
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v59
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology
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Call number:SPRINGER-2014-9783319017365:ONLINE Show nearby items on shelf
Title:A Differential Approach to Geometry [electronic resource] : Geometric Trilogy III
Author(s): Francis Borceux
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theoryand the preliminary a pproaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providingan integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions,not just those constructed from polynomials. During the 18th centu ry, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter thisfascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincar characteristics) associated with a surface gives you alot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry , the geometry that underlies the theory of relativity. The book is of interest to all those who teach classicaldifferential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to intuitively introduce students to the highly technical nature of this branch of mathematics, inparticular when preparing students for courses on relativity
Contents:Introduction
Preface
1.The Genesis of Differential Methods
2.Plane Curves
3.A Museum of Curves
4.Skew Curves
5.Local Theory of Surfaces
6.Towards Riemannian Geometry
7.Elements of Global Theory of Surfaces
Appendices: A.Topology
B.Differential Equations
Index
Bibliography
ISBN:9783319017365
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry
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Call number:SPRINGER-2014-9781493909254:ONLINE Show nearby items on shelf
Title:Commutative Algebra [electronic resource] : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions
Author(s): Marco Fontana
Sophie Frisch
Sarah Glaz
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point tofuture directions of rese arch in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics andresearch methods include Noetherian and non- Noetheri an ring theory as well as integer-valued polynomials and functions. Specific topics include: Homological dimensions of Prfer-like rings Quasi complete rings Total graphs of rings Properties of prime ideals over various rings Bases for integer-valued p olynomials Boolean subrings The portable property of domains Probabilistic topics inIntn(D) Closure operations in Zariski-Riemann spaces of valuation domains Stability of domains Non-Noetherian grade Homotopy in integer-valued polynomials Localiza tions of global propertiesof rings Topics in integral closure Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees ofthe conferen ce in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Grazconference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere
Contents:Preface
Weak global dimension of Prfer
like rings (K. Adarbeh, S
E. Kabbaj)
Quasi
complete semilocal rings and modules (D.D. Anderson)
On the total graph of a ring and its related graphs: A survey (A. Badawi)
Prime ideals in polynomials and power series rings over Noetherian domains
Integer
valued polynomials: Looking for regular bases (J
L. Chabert)
On Boolean subrings of rings (I. Chajda, G. Eigenthaler)
On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet
L'Hermitte)
The probability that Intn(D) is free (J. Elliott
ISBN:9781493909254
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology
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Call number:SPRINGER-2014-9781493906826:ONLINE Show nearby items on shelf
Title:k-Schur Functions and Affine Schubert Calculus [electronic resource]
Author(s): Thomas Lam
Luc Lapointe
Jennifer Morse
Anne Schilling
Mark Shimozono
Mike Zabrocki
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads ofcombinatorics, geome try, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostlycombinatorial branch of symmetric function the ory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This isthe first introductory text on this subject. It contains many examp les in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advancedundergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field
Contents:1. Introduction
2. Primer on k
Schur Functions
3. Stanley symmetric functions and Peterson algebras
4. Affine Schubert calculus
ISBN:9781493906826
Series:eBooks
Series:SpringerLink
Series:Fields Institute Monographs, 1069-5273 : v33
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Combinatorics , Algebraic topology
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Call number:SPRINGER-2014-9781447154969:ONLINE Show nearby items on shelf
Title:Morse Theory and Floer Homology [electronic resource]
Author(s): Michle Audin
Mihai Damian
Date:2014
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the numberof 1-periodic trajecto ries of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool ofdifferential topology. It defines the Morse complex a nd the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology isan infinite-dimensional analogue of Morse homology. Its involvement has bee n crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology aremore intricate and imply the use of more sophisticated analytical methods, all of which are expla ined in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. Thebook originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercis es. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students
Contents:Introduction to Part I
Morse Functions
Pseudo
Gradients
The Morse Complex
Morse Homology, Applications
Introduction to Part II
What You Need To Know About Symplectic Geometry
The Arnold Conjecture and the Floer Equation
The Maslov Index
Linearization and Transversality
Spaces of Trajectories
From Floer To Morse
Floer Homology: Invariance
Elliptic Regularity
Technical Lemmas
Exercises for the Second Part
Appendices: What You Need to Know to Read This Book
ISBN:9781447154969
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Global differential geometry , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9788847028357:ONLINE Show nearby items on shelf
Title:Spectral Theory and Quantum Mechanics [electronic resource] : With an Introduction to the Algebraic Formulation
Author(s): Valter Moretti
Date:2013
Publisher:Milano : Springer Milan : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given tospectral theory features t hat are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in oneplace a number of useful rigorous statements on t he mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out toMaster's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. Thebook should benefit established researchers to organise and present the profusion of advanced ma terial disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly
Note:Springer eBooks
Contents:Introduction and mathematical backgrounds
Normed and Banach spaces, examples and applications
Hilbert spaces and bounded operators
Families of compact operators on Hilbert spaces and fundamental properties
Densely
defined unbounded operators on Hilbert spaces
Phenomenology of quantum systems and Wave Mechanics: an overview
The first 4 axioms of QM: propositions, quantum states and observables
Spectral Theory I: generalities, abstract C
algebras and operators in B(H)
Spectral theory II: unbounded operators on Hilbert spaces
Spectral Theory III: applications
Mathem
ISBN:9788847028357
Series:e-books
Series:SpringerLink (Online service)
Series:UNITEXT, 2038-5714
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Mathematical physics
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Call number:SPRINGER-2013-9783642393686:ONLINE Show nearby items on shelf
Title:Geometry of Continued Fractions [electronic resource]
Author(s): Oleg Karpenkov
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest inmultidimensional generalizati ons of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometricvision of continued fractions. It covers several appli cations to questions related tosuch areas asDiophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress inthe geometric theory of multidimensional continued fractions accompanied by current ly open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful forundergraduate or graduate courses
Note:Springer eBooks
Contents:Preface
Introduction
Part 1. Regular continued fractions: Chapter 1. Classical notions and definitions
Chapter 2. On integer geometry
Chapter 3. Geometry of regular continued fractions
Chapter 4. Complete invariant of integer angles
Chapter 5. Integer trigonometry for integer angles
Chapter 6. Integer angles of integer triangles
Chapter 7. Continued fractions and SL(2 Z) conjugacy classes. Elements of Gauss Reduction Theory. Markoff spectrum
Chapter 8. Lagrange theorem
Chapter 9. Gauss
Kuzmin statistics
Chapter 10. Geometric approximation aspects
Chapter 11
ISBN:9783642393686
Series:e-books
Series:SpringerLink (Online service)
Series:Algorithms and Computation in Mathematics, 1431-1550 : v26
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Discrete groups , Number theory
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Call number:SPRINGER-2013-9783642343643:ONLINE Show nearby items on shelf
Title:A Guide to the Classification Theorem for Compact Surfaces [electronic resource]
Author(s): Jean Gallier
Dianna Xu
Date:2013
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those withoutdetailed background know ledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy andformal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be awork-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincar characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learningwhere it is required, without interrupting the carefully planned structure of the core expositi on. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuineconfidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and val uable techniques available in algebraic topology
Note:Springer eBooks
Contents:The Classification Theorem: Informal Presentation
Surfaces
Simplices, Complexes, and Triangulations
The Fundamental Group, Orientability
Homology Groups
The Classification Theorem for Compact Surfaces
Viewing the Real Projective Plane in R3
Proof of Proposition 5.1
Topological Preliminaries
History of the Classification Theorem
Every Surface Can be Triangulated
Notes
ISBN:9783642343643
Series:e-books
Series:SpringerLink (Online service)
Series:Geometry and Computing, 1866-6795 : v9
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2013-9783319002576:ONLINE Show nearby items on shelf
Title:The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups [electronic resource]
Author(s): Daciberg Lima Goncalves
John Guaschi
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 manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks animportant step in th e computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysisof their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups.This manuscript will serve as a reference for the study of bra id groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra
Note:Springer eBooks
Contents:Introduction and statement of the main results
Virtually cyclic groups: generalities, reduction and the mapping class group
Realisation of the elements of V1(n) and V2(n) in Bn(S2)
Appendix: The subgroups of the binary polyhedral groups
References.
ISBN:9783319002576
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory , Algebraic topology
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Call number:SPRINGER-2013-9781461484684:ONLINE Show nearby items on shelf
Title:Rational Homotopy Theory and Differential Forms [electronic resource]
Author(s): Phillip Griffiths
John Morgan
Date:2013
Edition:2nd ed. 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:Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now The appearance ofthe text in book form is hi ghly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature. Zentralblatt MATH(Review of First Edition) The monograph is intended as a n introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty ofexamples, illustrations, diagrams and exercises. The material is developed with patienc e and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and itspower are elegantly presented. This is an excellent monograph. Bulletin of the American Mathematical Society (Review of First Edition) This completely revised and corrected version of the well-known Florence notes circulatedby the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov to wers and rational homotopy theory. This is then followed by an in-depth look at differentialforms and de Thams theorem on simplical complexes. In addition, Sullivans results on computing the rational homotopy type from forms is presented. New to the Seco nd Edition: *Fully-revised appendices including an expandeddiscussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With i ts modern approach and timelyrevisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and re
Note:Springer eBooks
Contents:1 Introduction
2 Basic Concepts
3 CW Homology Theorem
4 The Whitehead Theorem and the Hurewicz Theorem
5 Spectral Sequence of a Fibration
6 Obstruction Theory
7 Eilenberg
MacLane Spaces, Cohomology, and Principal Fibrations
8 Postnikov Towers and Rational Homotopy Theory
9 deRham's theorem for simplicial complexes
10 Differential Graded Algebras
11 Homotopy Theory of DGAs
12 DGAs and Rational Homotopy Theory
13 The Fundamental Group
14 Examples and Computations
15 Functorality
16 The Hirsch Lemma
17 Quillen's work on Rational Homotopy Theory
ISBN:9781461484684
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics, 0743-1643 : v16
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Topology , Algebraic topology
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Call number:SPRINGER-2013-9781461474227:ONLINE Show nearby items on shelf
Title:The Mathematical Structure of Classical and Relativistic Physics [electronic resource] A General Classification Diagram
Author(s): Enzo Tonti
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:The theoriesdescribing seemingly unrelated areas of physics have surprising analogies that have arousedthe curiosity of scientists and motivatedefforts toidentify reasons for their existence.Comparative study ofphysical theories has revealed the pres ence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physicsis the first book to analyzethis structure in depth, thereby exposing therelationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows oneto construct a classification diagram for variables, equations, and other theoretical characteristics. The bookis divided into three parts. The first introduces the framework for the above-mentioned classification, methodicallydevelopingageometric and topologicalformulationapplicable to allphysical laws and properties the second applies t his formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics,heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories. Suitable for a diverse audience of physicists, engineers, andmathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Written at alevel accessible t o graduate and advanced undergraduatestudents inmathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursew ork
Note:Springer eBooks
Contents:1 Introduction
Part I Analysis of variables and equations
2 Terminology revisited
3 Space and time elements and their orientation
4 Cell complexes
5 Analysis of physical variables
6 Analysis of physical equations
7 Algebraic topology
8 The birth of the classification diagrams
Part II Analysis of physical theories
9 Particle dynamics
10 Electromagnetism
11 Mechanics of deformable solids
12 Mechanics of fluids
13 Other physical theories
Part III Advanced analysis
14 General structure of the diagrams
15 The mathematical structure
Part IV Appen
ISBN:9781461474227
Series:e-books
Series:SpringerLink (Online service)
Series:Modeling and Simulation in Science, Engineering and Technology, 2164-3679
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial , Algebraic topology , Mathematical physics
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Call number:SPRINGER-2013-9781461469711:ONLINE Show nearby items on shelf
Title:Graphs on Surfaces [electronic resource] : Dualities, Polynomials, and Knots
Author(s): Joanna A Ellis-Monaghan
Iain Moffatt
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate theinterdependency between dualit y, medial graphs and knots how this interdependency is reflected in algebraic invariants of graphs and knots and how it can be exploited to solve problems in graph and knot theory. Taking aconstructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructionsto obtain full extensions of them to embedded graphs. The authors demonstrate the bene fits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces:Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knottheorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students an d researchers in either area. Because the area is advancing so rapidly, the authors give acomprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages ofconsidering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise
Note:Springer eBooks
Contents:1. Embedded Graphs
2. Generalised Dualities
3. Twisted duality, cycle family graphs, and embedded graph equivalence
4. Interactions with Graph Polynomials
5. Applications to Knot Theory
References
Index
ISBN:9781461469711
Series:e-books
Series:SpringerLink (Online service)
Series:SpringerBriefs in Mathematics, 2191-8198
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topology , Algebraic topology
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Call number:SPRINGER-2013-9781461459620:ONLINE Show nearby items on shelf
Title:Foundations of Abstract Analysis [electronic resource]
Author(s): Jewgeni H Dshalalow
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presentedin a self-contained wa y suitable both for classroom use and for self-study. While this book carries the rigor of advancedmodern analysis texts, it elaborates the material in much greater details and therefore fills a gap betweenintroductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of thepotential overload of new words, definitions, and concepts, the book (in its u nique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded byinformal discussions and blueprints followed by thorough details andsupported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of thebook, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. P rerequisites include advanced calculus, linear algebra, complex variables, and calculus basedprobability
Note:Springer eBooks
Contents:Set
Theoretic and Algebraic Preliminaries
Analysis of Metric Spaces
Elements of Point
Set Topology
Measurable Spaces and Measurable Functions
Measures
Integration in Abstract Spaces
Solutions to Selected Problems
Bibliography
List of Symbols
Index of Names and Terms
ISBN:9781461459620
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Numerical analysis
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Call number:SPRINGER-2013-9780817683979:ONLINE Show nearby items on shelf
Title:Groupoid Metrization Theory [electronic resource] : With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis
Author(s): Dorina Mitrea
Irina Mitrea
Marius Mitrea
Sylvie Monniaux
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. Thepresentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spacesand Functional Analysis include: * treatment of metri zation from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields * coverage of topics applicable to a variety of scientific areaswithin pure mathematics * useful techniques and extensive reference material * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be auseful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology andmetric properties and/or functional analysis and metric properties
Note:Springer eBooks
Contents:Introduction
Semigroupoids and Groupoids
Quantitative Metrization Theory
Applications to Analysis on Quasi
Metric Spaces
Non
Locally Convex Functional Analysis
Functional Analysis on Quasi
Pseudonormed Groups
References
Symbol Index
Subject Index
Author Index
ISBN:9780817683979
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Global analysis (Mathematics) , Harmonic analysis , Functional analysis , Topology
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Call number:SPRINGER-2013-9780817683641:ONLINE Show nearby items on shelf
Title:Configurations from a Graphical Viewpoint [electronic resource]
Author(s): Toma Pisanski
Brigitte Servatius
Date:2013
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. Inthis self-contained tex tbook, algebraic graph theory is used to introduce groups topological graph theory is used to explore surfaces and geometric graph theory is implemented to analyze incidence geometries. After a preview ofconfigurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied.Geometric aspects, some historical remarks, references, and applicationsof classicalconfigurationsappear in the last chapter. With over two hundred illustrations, challenging exercises at t he end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint iswell suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicia ns and researchers
Note:Springer eBooks
Contents:Preface
Introduction
Graphs
Groups, Actions, and Symmetry
Maps
Combinatorial Configurations
Geometric Configurations
Index
Bibliography
ISBN:9780817683641
Series:e-books
Series:SpringerLink (Online service)
Series:Birkhuser Advanced Texts Basler Lehrbcher
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Combinatorics , Geometry , Topology
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Call number:SPRINGER-2012-9783642303623:ONLINE Show nearby items on shelf
Title:Algebraic Operads [electronic resource]
Author(s): Jean-Louis Loday
Bruno Vallette
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
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Note:In many areas of mathematics some higher operations are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key tounderstanding and comparing them, to cre ating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such asalgebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study allkinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a concept ual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality forassociative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiarwith elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and num erous figures are included. After an elementary chapter on classical algebra, accessible toundergraduate students,the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three ap pendices review the basic results needed in order to understand thevarious chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, thebook can also be used as a reference work by researchers.
Note:Springer eBooks
Contents:Preface
1.Algebras, coalgebras, homology
2.Twisting morphisms
3.Koszul duality for associative algebras
4.Methods to prove Koszulity of an algebra
5.Algebraic operad
6 Operadic homological algebra
7.Koszul duality of operads
8.Methods to prove Koszulity of an operad
9.The operads As and A\infty
10.Homotopy operadic algebras
11.Bar and cobar construction of an algebra over an operad
12.(Co)homology of algebras over an operad
13.Examples of algebraic operads
Apendices: A.The symmetric group
B.Categories
C.Trees
References
Index
List of Not
ISBN:9783642303623
Series:e-books
Series:SpringerLink (Online service)
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v346
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Algebraic topology , Cell aggregation Mathematics
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Call number:SPRINGER-2012-9783642295140:ONLINE Show nearby items on shelf
Title:A1-Algebraic Topology over a Field [electronic resource]
Author(s): Fabien Morel
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
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Note:This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It isa natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to theproperties and computations of A1-homotopy sheaves, A1-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties
Note:Springer eBooks
Contents:1 Introduction
2 Unramified sheaves and strongly A1
invariant sheaves
3 Unramified Milnor
Witt K
theories
4 Geometric versus canonical transfers
5 The Rost
Schmid complex of a strongly A1
invariant sheaf
6 A1
homotopy sheaves and A1
homology sheaves
7 A1
coverings
8 A1
homotopy and algebraic vector bundles
9 The affine B.G. property for the linear groups and the Grassmanian
ISBN:9783642295140
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2052
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , K-theory , Algebraic topology
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Call number:SPRINGER-2012-9783642239052:ONLINE Show nearby items on shelf
Title:The Arithmetic of Fundamental Groups [electronic resource] PIA 2010
Author(s): Jakob Stix
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:In the more than 100 years since the fundamental group was first introduced by Henri Poincar it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, thisessential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought togethermathematicians who use or study fundamental gr oups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, -adic, p-adic, pro-algebraic andmotivic. It explores a wealth of topics that range from anabelian geomet ry (in particular the section conjecture), the -adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, andrelative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty metho d and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting,as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tams Szamuely, respectively
Note:Springer eBooks
ISBN:9783642239052
Series:e-books
Series:SpringerLink (Online service)
Series:Contributions in Mathematical and Computational Sciences : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Number theory , Topology
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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: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-2012-9783642192258:ONLINE Show nearby items on shelf
Title:A Royal Road to Algebraic Geometry [electronic resource]
Author(s): Audun Holme
Date:2012
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to readall of his work Eleme nts. Euclid is said to have answered: There is no royal road to geometry! The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royalroad to algebraic geometry. From a point of depart ure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendiecks theory of schemes. Contemporary homological tools areexplained. The reader will follow a directed path leading up to the main elem ents of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to awonderful field of research. The greatest scientific experience of a lifetime!
Note:Springer eBooks
Contents:Part I Curves: 1 Affine and Projective Space
2 Curves in A2 k and in P2
3 Higher Geometry in the Projective Plane
4 Plane Curves and Algebra
5 Projective Varieties in PNk
Part II Introduction to Grothendiecks Theory of Schemes: 6 Categories and Functors
7 Constructions and Representable Functors
8 Abelian Categories
9 The Concept of Spec(A)
10 The Category of Schemes
11 Properties of Morphisms of Schemes
12 Modules, Algebras and Bundles on a Scheme
13 More Properties of Morphisms, Scheme Theoretic Image and the Sorite
14 Projective Schemes and Bu
ISBN:9783642192258
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Geometry , Algebraic topology
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Call number:SPRINGER-2012-9783034804936:ONLINE Show nearby items on shelf
Title:Plane Algebraic Curves [electronic resource] : Translated by John Stillwell
Author(s): Egbert Brieskorn
Horst Knrrer
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source ofinspiration and topic of resear ch to this day. Arising from notes for a course given at the University of Bonn in Germany, Plane Algebraic Curves reflects the authors concern for the student audience through emphasis uponmotivation, development of imagination, and understanding of basi c ideas. As classical objects, curves may be viewed from many angles this text provides a foundation for the comprehension and exploration of modern work onsingularities. --- In the first chapter one finds many special curves with very attractive geometr ic presentations the wealth of illustrations is a distinctive characteristic of this book and an introduction toprojective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezouts theorem and a detailed discuss ion of cubics. The heart of this book and how else could it be with the first author is the chapter on the resolution of singularities (always over the complex numbers). () Especially remarkable is the outlook to further work on the topics discussed, wit h numerous references to the literature. Many examplesround off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)
Note:Springer eBooks
Contents:I. History of algebraic curves
1. Origin and generation of curves
2. Synthetic and analytic geometry
3. The development of projective geometry
II. Investigation of curves by elementary algebraic methods
4. Polynomials
5. Definition and elementary properties of plane algebraic curves
6. The intersection of plane curves
7. Some simple types of curves
III. Investigation of curves by resolution of singularities
8. Local investigations
9. Global investigations
Bibliography
Index
ISBN:9783034804936
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Algebra , Algebraic topology
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Call number:SPRINGER-2012-9783034804059:ONLINE Show nearby items on shelf
Title:Associahedra, Tamari Lattices and Related Structures [electronic resource] : Tamari Memorial Festschrift
Author(s): Folkert Mller-Hoissen
Jean Marcel Pallo
Jim Stasheff
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
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Note:Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. Thiswas the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematicalwork. Tamari lattices ca n be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure andapplied mathematics, such as algebra, combinator ics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari'scentennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers inmathematics and mathematical physics and are accompanied by high quality illustrations
Note:Springer eBooks
ISBN:9783034804059
Series:e-books
Series:SpringerLink (Online service)
Series:Progress in Mathematics : v299
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Discrete groups , Number theory , Algebraic topology
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Call number:SPRINGER-2012-9781461419396:ONLINE Show nearby items on shelf
Title:Spectra of Graphs [electronic resource]
Author(s): Andries E Brouwer
Willem H Haemers
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
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Note:This book provides an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. It covers standard topics such as bounds on the sizes of cliques and cocliques, chromaticnumber and Shannon capac ity, the connection between randomness and the 'eigenvalue gap', and applications. It continues with a presentation of some new material on trees, strongly regular graphs, two-graphs, association schemes,p-ranks of configurations and similar topics. Exerc ises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, referencesat the end of the book, an author and subject index enrich the text. Spect ra of Graphs is written for researchers, teachers and students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra andeigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theo rem and eigenvalue interlacing are included
Note:Springer eBooks
Contents:Graph spectrum
Linear algebra
Eigenvalues and eigenvectors of graphs
The second largest eigenvalue
Trees
Groups and graphs
Topology
Euclidean representations
Strongly regular graphs
Regular two
graphs
Association schemes
Distance regular graphs
p
ranks
Spectral characterizations
Graphs with few eigenvalues
References
Author Index
Subject Index
ISBN:9781461419396
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Group theory
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Call number:SPRINGER-2012-9781461418979:ONLINE Show nearby items on shelf
Title:Topological Aspects of Nonsmooth Optimization [electronic resource]
Author(s): Vladimir Shikhman
Date:2012
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This bookdeals withnonsmooth structures arising within the optimization setting. It considers four optimization problems, namely,mathematical programs with complementarity constraints, general semi-infinite programmingproblems, mathematical programs with vanishing constraints andbilevel optimization. The author uses thetopologicalapproachand topological invariants of corresponding feasible sets are investigated.Moreover, the critical pointtheory in the sense of Morse is presented and parametric and s tability issues are considered.The material progresses systematically andestablishesacomprehensive theory for a rather broad class of optimization problems tailoredto theirparticular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization wi ll benefit researchers and graduate studentsin applied mathematics, especially those workingin optimization theory, nonsmooth analysis,algebraic topology and singularity theory
Note:Springer eBooks
Contents:Preface
Notation
Introduction
Mathematical Programming Problems with Complementarity
Constraints
General Semi
infinite Programming Problems
Mathematical Programming Problems with Vanishing Constraints
Bilevel Optimization
Impacts on Nonsmooth Analysis
Appendix
Bibliography
References
Index
ISBN:9781461418979
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Optimization and Its Applications, 1931-6828 : v64
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Mathematical optimization
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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
Note:Springer e-book platform
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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-2012-9781447143932:ONLINE Show nearby items on shelf
Title:The Local Structure of Algebraic K-Theory [electronic resource]
Author(s): Bjrn Ian Dundas
Thomas G Goodwillie
Randy McCarthy
Date:2012
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
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Note:Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerfulmathematical object is ve ry hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homologicalinvariants offered by motivic cohomology and topo logical cyclic homology. This book covers the connection between algebraic K-theory and Bkstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference betweenthe theories are locally constant. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain ahost of nearby calculations in K-theory. For instance, Quillen's calculation of the K-theory of fini te fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers giveinsight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local corresponden ce between K-theory and topological cyclic homology, the book provides an introduction to the necessarybackground in algebraic K-theory and highly structured homotopy theory collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in thefield. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology
Note:Springer eBooks
Contents:Algebraic K
theory
Gamma
spaces and S
algebras
Reductions
Topological Hochschild Homology
The Trace K THH
Topological Cyclic Homology
The Comparison of K
theory and TC
ISBN:9781447143932
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications, 1572-5553 : v18
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , K-theory , Algebraic topology
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Call number:SPRINGER-2012-9781447122944:ONLINE Show nearby items on shelf
Title:Syzygies and Homotopy Theory [electronic resource]
Author(s): F.E.A Johnson
Date:2012
Publisher:London : Springer London
Size:1 online resource
Note:Springer e-book platform
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Note:The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology
Note:Springer eBooks
Contents:Preliminaries
The restricted linear group
The calculus of corners and squares
Extensions of modules
The derived module category
Finiteness conditions
The Swan mapping
Classification of algebraic complexes
Rings with stably free cancellation
Group rings of cyclic groups
Group rings of dihedral groups
Group rings of quaternionic groups
Parametrizing W1 (Z) : generic case
Parametrizing W1 (Z) : singular case
Generalized Swan modules
Parametrizing W1 (Z) : G = C F
Conclusion
ISBN:9781447122944
Series:e-books
Series:SpringerLink (Online service)
Series:Algebra and Applications, 1572-5553 : v17
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Group theory
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Call number:SPRINGER-2012-9780817683436:ONLINE Show nearby items on shelf
Title:Singularities of Differentiable Maps, Volume 2 [electronic resource] : Monodromy and Asymptotics of Integrals
Author(s): V.I Arnold
S.M Gusein-Zade
A.N Varchenko
Date:2012
Publisher:Boston : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
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Note:Originally published inthe 1980s, Singularities of DifferentiableMaps: Monodromy and Asymptotics of Integrals was thesecond oftwovolumes that togetherformed a translation of the authors'influential Russian monographon singularity theory.This uncorrec ted softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience of researchers and practitioners. Whilethe first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable mapsthat is, was devoted to a description of what, where, and how singularities could beencounteredthis second volume concentrates on elements of theanatomy and physiology of singu larities of differentiable functions. The questions considered here are about the structure of singularities and how they function. Inthe first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanis hing cycles distinguished bases intersection matricesmonodromy groupsthe variation operatorand theirinterconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary pha se, which is widely met within applications. The third and last part dealswith integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. Thismonograph is suitablefor mathematicians, researchers, postgradua tes, and specialists in the areas ofmechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps
Note:Springer eBooks
Contents:Part I. The topological structure of isolated critical points of functions
Introduction
Elements of the theory of Picard
Lefschetz
The topology of the non
singular level set and the variation operator of a singularity
The bifurcation sets and the monodromy group of a singularity
The intersection matrices of singularities of functions of two variables
The intersection forms of boundary singularities and the topology of complete intersections
Part II. Oscillatory integrals
Discussion of results
Elementary integrals and the resolution of singularities of the phase
As
ISBN:9780817683436
Series:e-books
Series:SpringerLink (Online service)
Series:Modern Birkhuser Classics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics
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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
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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-2012-9780387847948: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-2011-9783642225345:ONLINE Show nearby items on shelf
Title:Pseudo-periodic Maps and Degeneration of Riemann Surfaces [electronic resource]
Author(s): Yukio Matsumoto
Jos Mara Montesinos-Amilibia
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. Inthis book, the conjuga cy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsens incomplete classification is corrected. The second part applies the results of the first part to the topologyof degeneration of Riemann surfaces. It is show n that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set ofconjugacy classes of the pseudo-periodic maps of negative twists. The corres pondence is given by the topological monodromy
Note:Springer eBooks
Contents:Part I: Conjugacy Classification of Pseudo
periodic Mapping Classes
1 Pseudo
periodic Maps
2 Standard Form
3 Generalized Quotient
4 Uniqueness of Minimal Quotient
5 A Theorem in Elementary Number Theory
6 Conjugacy Invariants
Part II: The Topology of Degeneration of Riemann Surfaces
7 Topological Monodromy
8 Blowing Down Is a Topological Operation
9 Singular Open
Book
ISBN:9783642225345
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2030
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , Cell aggregation Mathematics
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Call number:SPRINGER-2011-9783642220036:ONLINE Show nearby items on shelf
Title:Algebraic Topology of Finite Topological Spaces and Applications [electronic resource]
Author(s): Jonathan A Barmak
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
Note:Springer e-book platform
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Note:This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makesfinite spaces a usefu l tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillens conjecture on the poset of p-subgroups ofa finite group and the Andrews-Curtis conjec ture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It isintended for topologists and combinatorialists, but it is also recom mended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology
Note:Springer eBooks
Contents:1 Preliminaries
2 Basic topological properties of finite spaces
3 Minimal finite models
4 Simple homotopy types and finite spaces
5 Strong homotopy types
6 Methods of reduction
7 h
regular complexes and quotients
8 Group actions and a conjecture of Quillen
9 Reduced lattices
10 Fixed points and the Lefschetz number
11 The Andrews
Curtis conjecture
ISBN:9783642220036
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2032
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Algebra , Combinatorics , Discrete groups , Algebraic topology , Cell aggregation Mathematics
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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
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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-2011-9783642195808:ONLINE Show nearby items on shelf
Title:Topological Complexity of Smooth Random Functions [electronic resource] : cole d't de Probabilits de Saint-Flour XXXIX-2009
Author(s): Robert J Adler
Jonathan E Taylor
Date:2011
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors 2007 Springer monograph Random Fields and Geometry. While not as exhaustive as the full monograph, they are also lessexhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notesinclude an introduction to the general theory of Gaussian r andom fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis ontube formulae, to provide the reader with the material needed to understand and us e the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, bothof which provide applications of the main results
Note:Springer eBooks
Contents:1 Introduction
2 Gaussian Processes
3 Some Geometry and Some Topology
4 The Gaussian Kinematic Formula
5 On Applications: Topological Inference
6 Algebraic Topology of Excursion Sets: A New Challenge
ISBN:9783642195808
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2019
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry , Mathematical statistics
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