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Call number: | SPRINGER-2016-9783319392868:ONLINE Show nearby items on shelf |
Title: | Operator Algebras and Applications The Abel Symposium 2015 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (2 p.) |
Note: | 10.1007/978-3-319-39286-8 |
Contents: | C*-tensor categories and subfactors for totally disconnected groups: Y. Arano and S. Vaes -- Decomposable approximations revisited: N.P. Brown, J.R. Carrión and S. White -- Exotic crossed products: A. Buss, S. Echterhoff, and R. Willett -- On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra: T. M. Carlsen and A. Sims -- Commutator inequalities via Schur products: E. Christensen -- C*-algebras associated with algebraic actions: J. Cuntz -- A new look at C*-simplicit y and the unique trace property of a group: U. Haagerup -- Equilibrium states on graph algebras: A. an Huef and I. Raeburn -- Semigroup C_-algebras: X. Li -- Topological full groups of étale groupoids: H. Matui -- Towards a classification of compact quan tum groups of Lie type: S. Neshveyev and M. Yamashita -- A homology theory for Smale spaces: a summary: I.F. Putnam -- On the positive eigenvalues and eigenvectors of a non-negative matrix: K. Thomsen -- Classification of graph algebras: a |
selective survey: M. Tomforde -- QDQ vs. UCT: W. Winter | |
ISBN: | 9783319392868 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Abel Symposia: 12 |
Keywords: | Mathematics , K-theory , Dynamics , Ergodic theory , Functional analysis , Mathematical physics , Mathematics , Functional Analysis , Dynamical Systems and Ergodic Theory , K-Theory , Mathematical Physics |
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Call number: | SPRINGER-2016-9783319293516:ONLINE Show nearby items on shelf |
Title: | Bulk and Boundary Invariants for Complex Topological Insulators From K-Theory to Physics |
Author(s): |
Emil Prodan |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (204 p.) |
Note: | 10.1007/978-3-319-29351-6 |
Contents: | Illustration of key concepts in dimension d = 1 -- Topological solid state systems: conjectures, experiments and models -- Observables algebras for solid state systems -- K-theory for topological solid state systems -- The topological |
invariants and their interrelations -- Index theorems for solid state systems -- Invariants as measurable quantities | |
ISBN: | 9783319293516 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , K-theory , Mathematical physics , Solid state physics , Physics , Mathematical Methods in Physics , K-Theory , Mathematical Physics , Solid State Physics |
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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-2014-9783319081533:ONLINE Show nearby items on shelf |
Title: | Algebraic K-theory of Crystallographic Groups [electronic resource] : The Three-Dimensional Splitting Case |
Author(s): |
Daniel Scott Farley Ivonne Johanna Ortiz |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives apowerful method for comput ing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class ofthree-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifyingspaces. Later chapters assemble the techniques that are needed to apply the i somorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphismconjecture, and a contribution to the growing literature in the field |
ISBN: | 9783319081533 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2113 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , K-theory , Cell aggregation Mathematics |
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Call number: | SPRINGER-2014-9783034805100:ONLINE Show nearby items on shelf |
Title: | The Localization Problem in Index Theory of Elliptic Operators [electronic resource] |
Author(s): |
Vladimir Nazaikinskii Bert-Wolfgang Schulze Boris Sternin |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actuallya fundamental localiz ation principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of important newproblems in index theory. So far, the loca lization principle has scarcely been covered in journal papers. The present book is intended to fill this gap. Both the general localization principle and its applications to specific problems,old and new, are covered. Concisely and clearly written, this monograph includes numerous figures helping the reader to visualize the material. The Localization Problem in Index Theory of Elliptic Operators will be of interest toresearchers as well as graduate and postgraduate students specializing in differential e quations and related topics |
Contents: | Preface |
Introduction | |
0.1 Basics of Elliptic Theory | |
0.2 Surgery and the Superposition Principle | |
0.3 Examples and Applications | |
0.4 Bibliographical Remarks | |
Part I: Superposition Principle | |
1 Superposition Principle for the Relative Index | |
1.1 Collar Spaces | |
1.2 Proper Operators and Fredholm Operators | |
1.3 Superposition Principle | |
2 Superposition Principle for K | |
Homology | |
2.1 Preliminaries | |
2.2 Fredholm Modules and K | |
Homology | |
2.3 Superposition Principle | |
2.4 Fredholm Modules and Elliptic Operators | |
3 Superposition Principle for KK | |
Theory | |
3.1 Preliminaries | |
ISBN: | 9783034805100 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Pseudo-Differential Operators, Theory and Applications : v10 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Functional analysis , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2013-9783642321993:ONLINE Show nearby items on shelf |
Title: | Noncommutative Iwasawa Main Conjectures over Totally Real Fields [electronic resource] : Mnster, April 2011 |
Author(s): |
John Coates Peter Schneider R Sujatha Otmar Venjakob |
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: | The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.Non-commutative Iwas awa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field,independently by Ritter and Weiss on the one ha nd, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developedin the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fu kaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered animportant idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with anidea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The appro ach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideasin this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of s ome of the main general themes underlying these developments. The present volume will be a valuableresource for researchers working in both Iwasawa theory and the theory of automorphic forms. |
Note: | Springer eBooks |
Contents: | Preface |
John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the non | |
commutative main conjectures for totally real fields | |
R. Sujatha: Reductions of the main conjecture | |
Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present | |
Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde | |
Mahesh Kakde: Congruences between abelian p | |
adic zeta functions | |
Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach | |
Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory | |
ISBN: | 9783642321993 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Number theory |
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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-2013-9783319001289:ONLINE Show nearby items on shelf |
Title: | Hypoelliptic Laplacian and BottChern Cohomology [electronic resource] : A Theorem of RiemannRochGrothendieck in Complex Geometry |
Author(s): |
Jean-Michel Bismut |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes inBottChern cohomology, which is a refi nement for complex manifolds of de Rham cohomology. When the manifolds are Khler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformationvia Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKeanSinger in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.Onetool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for thedeformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Whil e the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonicoscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea dev eloped in the book is that while classical elliptic Hodge theory is based on theHermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an imp ortant role, either as a motivation of some constructions,or in the proofs themselves |
Note: | Springer eBooks |
Contents: | Introduction |
1 The Riemannian adiabatic limit | |
2 The holomorphic adiabatic limit | |
3 The elliptic superconnections | |
4 The elliptic superconnection forms | |
5 The elliptic superconnections forms | |
6 The hypoelliptic superconnections | |
7 The hypoelliptic superconnection forms | |
8 The hypoelliptic superconnection forms of vector bundles | |
9 The hypoelliptic superconnection forms | |
10 The exotic superconnection forms of a vector bundle | |
11 Exotic superconnections and RiemannRochGrothendieck | |
Bibliography | |
Subject Index | |
Index of Notation. | |
ISBN: | 9783319001289 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-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 |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This text deals with A^{1}-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 A^{1}-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 A^{1-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-2012-9783034802574:ONLINE Show nearby items on shelf |
Title: | Metric and Differential Geometry [electronic resource] : The Jeff Cheeger Anniversary Volume |
Author(s): |
Xianzhe Dai Xiaochun Rong |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Metric and Differential Geometry grew out ofa similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions in this volume cover a broad range oftopics in metric and diffe rential geometry, including metric spaces, Ricci flow, Einstein manifolds, Khler geometry, index theory, and hypoelliptic Laplacian and analytic torsion. The book includes papers on the most recent advancesas well as survey articles on new developments. C ontributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Mller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W.Zhang |
Note: | Springer eBooks |
Contents: | Preface |
Blaine Lawson, Early Work of Jeff Cheeger | |
Mike Anderson, Boundary value problems for metrics on 3 | |
manifolds | |
Xiuxiong Chen and Song Sun, Space of Kaehler metrics (V) Kaehler quantization | |
Reese Harvey and Blaine Lawson, Split special Lagrangian geometry | |
Christina Sormani, How Riemannian manifolds converge: a survey | |
Gang Tian, Existence of Einstein metrics on Fano manifolds | |
Pekka Koskela and K. Wildrick, Analytic properties of quasiconformal mappings between metric spaces | |
Assaf Naor, An application of metric cotype to quasisymmetric embeddings | |
Jean | |
Michel Bi | |
ISBN: | 9783034802574 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v297 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Geometry , Global differential geometry |
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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 |
Note: | Springer e-book platform |
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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 |
Note: | Springer 2013 e-book collections |
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-2011-9783642217746:ONLINE Show nearby items on shelf |
Title: | From Objects to Diagrams for Ranges of Functors [electronic resource] |
Author(s): |
Pierre Gillibert Friedrich Wehrung |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This work introduces tools from the field of category theory that make it possible to tackle a number of representation problems that have remained unsolvable to date (e.g. the determination of the range of a given functor). Thebasic idea is: if a fu nctor lifts many objects, then it also lifts many (poset-indexed) diagrams |
Note: | Springer eBooks |
Contents: | 1 Background |
2 Boolean Algebras Scaled with Respect to a Poset | |
3 The Condensate Lifting Lemma (CLL) | |
4 Larders from First | |
order Structures | |
5 Congruence | |
Preserving Extensions | |
6 Larders from von Neumann Regular Rings | |
7 Discussion | |
ISBN: | 9783642217746 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2029 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Logic, Symbolic and mathematical |
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Call number: | SPRINGER-2011-9783642157080:ONLINE Show nearby items on shelf |
Title: | Topics in Algebraic and Topological K-Theory [electronic resource] |
Author(s): |
Paul Frank Baum Guillermo Cortias Ralf Meyer Rubn Snchez-Garca Marco Schlichting Bertrand Ton |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparisonbetween algebraic and top ological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories |
Note: | Springer eBooks |
Contents: | K |
theory for group C* | |
algebras | |
Universal Coefficient Theorems and assembly maps in KK | |
theory | |
Algebraic v. topological K | |
theory: a friendly match | |
Higher algebraic K | |
theory (after Quillen, Thomason and others) | |
Lectures on DG | |
categories | |
ISBN: | 9783642157080 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2008 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory |
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Call number: | SPRINGER-2010-9783642112973:ONLINE Show nearby items on shelf |
Title: | Biset Functors for Finite Groups [electronic resource] |
Author(s): |
Serge Bouc |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume exposes the theory of biset functors for finite groups, which yields a unified framework for operations of induction, restriction, inflation, deflation and transport by isomorphism. The first part recalls the basics onbiset categories and biset functors. The second part is concerned with the Burnside functor and the functor of complex characters, together with semisimplicity issues and an overview of Green biset functors. The last part is devoted tobiset functors defined over p-groups for a fixed prime number p. This includes the structure of the functor of rational representations and rational p-biset functors. The last two chapters expose three applications of biset functors tolong-standing open problems, in particular the structure of the Dade group of an arbitrary finite p-group.This book is intended both to students and researchers, as it gives a didactic exposition of the basics and a rewriting ofadvanced results in the area, with some new ideas and proofs |
Note: | Springer eBooks |
Contents: | 1 Examples |
Part I General properties | |
2 G | |
sets and (H,G) | |
bisets | |
3 Biset functors | |
4 Simple functors | |
Part II Biset functors on replete subcategories | |
5 The Burnside functor | |
6 Endomorphism algebras | |
7 The functor CRC | |
8 Tensor product and internal hom | |
Part III p | |
biset functors | |
9 Rational representations of p | |
groups | |
10 p | |
biset functors | |
11 Applications | |
12 The Dade group | |
ISBN: | 9783642112973 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1990 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , K-theory |
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Call number: | SPRINGER-2010-9783034605656:ONLINE Show nearby items on shelf |
Title: | Homotopy Theory of C*-Algebras [electronic resource] |
Author(s): |
Paul Arne stvr |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraictopology into one catego ry comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitionsof invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopytheory and applications |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Preliminaries | |
2.1 C* | |
spaces | |
2.2 G C* | |
spaces | |
2.3 Model categories | |
3 Unstable C* | |
homotopy theory | |
3.1 Pointwise model structures | |
3.2 Exact model structures | |
3.3 Matrix invariant model structures | |
3.4 Homotopy invariant model structures | |
3.5 Pointed model structures | |
3.6 Base change | |
4 Stable C* | |
homotopy theory | |
4.1 C* | |
spectra | |
4.2 Bispectra | |
4.3 Triangulated structure | |
4.4 Brown representability | |
4.5 C* | |
symmetric spectra | |
4.6 C* | |
functors | |
5 Invariants | |
5.1 Cohomology and homology theories | |
5.2 KK | |
theory and the Eilenberg | |
MacLan | |
ISBN: | 9783034605656 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Algebraic topology |
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Call number: | SPRINGER-2010-9780817649388:ONLINE Show nearby items on shelf |
Title: | Representation Theory and Complex Geometry [electronic resource] |
Author(s): |
Neil Chriss Victor Ginzburg |
Date: | 2010 |
Edition: | 1st |
Publisher: | Boston : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since thediscovery of D-module s in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Liegroups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. The book is largelyself-contained. . . . There is a nice introduction to symplectic geometry and a cha rming exposition of equivariant K-theory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey someinformal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it hasalready proved successful in introducing a new generation to the subject. --- Bulletin of the American Mathematical Society Th e authors have tried to help readers by adopting an informal and easily accessible style. . . . The book willprovide a guide to those who wish to penetrate into subject-matter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of oneof the chapters of the book. --- Mededelingen van het Wiskundig Genootschap Represents an important and very interesting addition to the literature. --- Mathematical R eviews |
Note: | Springer eBooks |
Contents: | Preface |
Chapter 0. Introduction | |
Chapter 1. Symplectic Geometry | |
Chapter 2. Mosaic | |
Chapter 3. Complex Semisimple Groups | |
Chapter 4. Springer Theory | |
Chapter 5. Equivariant K | |
Theory | |
Chapter 6. Flag Varieties, K | |
Theory, and Harmonic Polynomials | |
Chapter 7. Hecke Algebras and K | |
Theory | |
Chapter 8. Representations of Convolution Algebras | |
Bibliography | |
ISBN: | 9780817649388 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Topological Groups , Cell aggregation Mathematics |
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Call number: | SPRINGER-2009-9783642012006:ONLINE Show nearby items on shelf |
Title: | Algebraic Topology [electronic resource] : The Abel Symposium 2007 |
Author(s): |
Nils Baas Eric M Friedlander Bjrn Jahren Paul Arne stvr |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraicK-theory, algebraic topolog y, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of thisvolume demonstrate, these perspectives and constr uctions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new |
Note: | Springer eBooks |
Contents: | The Classifying Space of a Topological 2 |
Group | |
String Topology in Dimensions Two and Three | |
Floer Homotopy Theory, Realizing Chain Complexes by Module Spectra, and Manifolds with Corners | |
Relative Chern Characters for Nilpotent Ideals | |
Algebraic Differential Characters of Flat Connections with Nilpotent Residues | |
Norm Varieties and the Chain Lemma (After Markus Rost) | |
On the Whitehead Spectrum of the Circle | |
Cocycle Categories | |
A Survey of Elliptic Cohomology | |
On Voevodsky's Algebraic | |
Theory Spectrum | |
Chern Character, Loop Spaces and Derived Algebraic Geometry | |
Voevodsk | |
ISBN: | 9783642012006 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia : v4 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Algebraic topology , Mathematical physics |
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Call number: | SPRINGER-2009-9783034601894:ONLINE Show nearby items on shelf |
Title: | Simplicial Homotopy Theory [electronic resource] |
Author(s): |
Paul G Goerss John F Jardine |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed modelcategory and, in particula r, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, includingalgebraic K-theory. This book supplies a modern e xposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups,Postnikov towers, and bisimplicial sets. The more advanced material in cludes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence.Interspersed throughout are many results and ideas well-known to experts, but uncollected in the lit erature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory.An extensive background in topology is not assumed. Reviews: a book filling an obvious gap in the literature and the au thors have done an excellent job on it. No monograph or expository paper has been published on this topic inthe last twenty-eight years. - Analele Universitatii din Timisoara is clearly presented and a brief summary preceding every chapter is useful to t he reader. The book should prove enlightening to a broad range of readersincluding prospective students and researchers who want to apply simplicial techniques for whatever reason. - Zentralblatt MATH they succeed. The book is an excellent account of sim plicial homotopy theory from a modern point ofview [] The book is well written. [] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques |
Note: | Springer eBooks |
ISBN: | 9783034601894 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf |
Title: | Polytopes, Rings, and K-Theory [electronic resource] |
Author(s): |
Joseph Gubeladze Winfried Bruns |
Date: | 2009 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University |
Note: | Springer eBooks |
Contents: | Preface |
Polytopes, cones, and complexes | |
Affine monoids and their Hilbert bases | |
Multiples of lattice polytopes | |
Monoid algebras | |
Isomorphisms and automorphisms | |
Homological properties and Hilbert functions | |
Grbner bases, triangulations, and Koszul algebras | |
Projective modules over monoid rings | |
Bass | |
Whitehead groups of monoid rings | |
Varieties | |
References | |
Notation | |
Index | |
ISBN: | 9780387763569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Discrete groups |
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Call number: | SPRINGER-2008-9783764387754:ONLINE Show nearby items on shelf |
Title: | Elliptic Theory and Noncommutative Geometry [electronic resource] : Nonlocal Elliptic Operators |
Author(s): |
Vladimir E Nazaikinskii Anton Yu Savin Boris Yu Sternin |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This comprehensive yet concise book deals with nonlocal elliptic differential operators, whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of thestudy is to relate analyt ical invariants (in particular, the index) of such elliptic operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. This is the firstand so far the only book featuring a consiste nt application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. Although the book provides important results, which are in a sensedefinitive, on the above-mentioned topic, it contains all the necessa ry preliminary material, such as C*-algebras and their K-theory or cyclic homology. Thus the material is accessible for undergraduate students of mathematics (thirdyear and beyond). It is also undoubtedly of interest for post-graduate students and scienti sts specializing in geometry, the theory of differential equations, functional analysis, etc. The book can serve as a good introduction tononcommutative geometry, which is one of the most powerful modern tools for studying a wide range of problems in math ematics and theoretical physics |
Note: | Springer eBooks |
ISBN: | 9783764387754 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications, Advances in Partial Differential Equations : v183 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory |
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Call number: | SPRINGER-2008-9783764386047:ONLINE Show nearby items on shelf |
Title: | C*-algebras and Elliptic Theory II [electronic resource] |
Author(s): |
Dan Burghelea Richard Melrose Alexander S Mishchenko Evgenij V Troitsky |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered includethe index of operator s, torsion invariants, K-theory of operator algebras and L2-invariants. The results presented in this book, which is largely inspired and stimulated by the Atiyah-Singer index theorem, should be of interest tograduates and researchers in mathematical phys ics, differential topology and differential analysis |
Note: | Springer eBooks |
Contents: | Preface |
Lefschetz Distribution of Lie Foliations | |
Torsion as Function on the Space of Representations | |
K | |
theory of Twisted Group Algebras | |
Twisted Burnside Theorem for Two | |
Step Torsion | |
free Nilpotent Groups | |
Ihara Zeta Functions for Periodic Simple Graphs | |
Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds | |
Non | |
standard Podle's Spheres | |
Elliptic Theory on Manifolds with Corners | |
Dixmier Traceability for General Pseudo | |
differential Operators | |
Topological Invariants of Bifurcation | |
L2 | |
Invariants and Rank Metric | |
Group Bundle Duality | |
A New Topolog | |
ISBN: | 9783764386047 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2008-9783540749561:ONLINE Show nearby items on shelf |
Title: | Basic Bundle Theory and K-Cohomology Invariants [electronic resource] : With contributions by Siegfried Echterhoff, Stefan Fredenhagen and Bernhard Krtz |
Author(s): |
D Husemller M Joachim B Juro M Schottenloher |
Date: | 2008 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamentaltheme, emphasized in t he book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comesfrom quantum field theory, especially strin g theory, where topological invariants play an important role |
Note: | Springer eBooks |
Contents: | Physical Background to the K |
Theory Classification of D | |
Branes: Introduction and References | |
Physical Background to the K | |
Theory Classification of D | |
Branes: Introduction and References | |
Bundles over a Space and Modules over an Algebra | |
Generalities on Bundles and Categories | |
Vector Bundles | |
Relation Between Vector Bundles, Projective Modules, and Idempotents | |
K | |
Theory of Vector Bundles, of Modules, and of Idempotents | |
Principal Bundles and Sections of Fibre Bundles: Reduction of the Structure and the Gauge Group I | |
Homotopy Classification of Bundles and Cohomology: Classifying | |
ISBN: | 9783540749561 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v726 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Algebra , Mathematical physics |
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Call number: | SPRINGER-2007-9783764383992:ONLINE Show nearby items on shelf |
Title: | Topological and Bivariant K-Theory [electronic resource] |
Author(s): |
Joachim Cuntz Ralf Meyer Jonathan M Rosenberg |
Date: | 2007 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it fromalgebraic K-theory. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. Asapplications, we study K-theory of crossed pr oducts, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem |
Note: | Springer eBooks |
Contents: | Preface |
The Elementary Algebra of K | |
theory | |
Functional Calculus and Topological K | |
theory | |
Homotopy Invariance of Stabilized Algebraic K | |
theory | |
Bott periodicity | |
K | |
theory of Crossed Products | |
Bivariant K | |
theory | |
Connections with Index Theory | |
Localization of Triangulated Categories | |
Algebras of Continuous Trace and Twisted K | |
theory | |
Connes' Thom Isomorphism | |
Applications to Physics | |
ISBN: | 9783764383992 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Oberwolfach Seminars : v36 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory |
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Call number: | SPRINGER-2007-9783540368243:ONLINE Show nearby items on shelf |
Title: | Algebraic Cobordism [electronic resource] |
Author(s): |
Marc Levine Fabien Morel |
Date: | 2007 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (incharacteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over theLazard ring by the elements of positive degrees. Th is implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications |
Note: | Springer eBooks |
Contents: | Introduction |
I. Cobordism and oriented cohomology | |
1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism | |
II. The definition of algebraic cobordism. 2.1. Oriented Borel | |
Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism | |
III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extende | |
ISBN: | 9783540368243 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , K-theory |
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Call number: | SPRINGER-2007-9780817645748:ONLINE Show nearby items on shelf |
Title: | The Grothendieck Festschrift [electronic resource] A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck |
Author(s): |
Pierre Cartier Luc Illusie Nicholas M Katz Grard Laumon Yuri I Manin Kenneth A Ribet |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The many diverse articles presented in these three volumes, collected on the occasion of Alexander Grothendiecks sixtieth birthday and originally published in 1990, were offered as a tribute to one of the worlds greatestliving mathematicians. Grothen dieck changed the very way we think about many branches of mathematics. Many of his ideas, revolutionary when introduced, now seem so natural as to have been inevitable. Indeed, it is difficult to fullygrasp the influence his vast contributions to modern mathematics have subsequently had on new generations of mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundationalto the subject. Topics addressed by these top-notch contributors match th e breadth of Grothendiecks own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory,K-theory, category theory, and homological algebra. CONTRIBUTORS to Volume I: A. Altman M. Artin V. Bala ji A. Beauville A.A. Beilinson P. Berthelot J.-M. Bismut S. Bloch L. Breen J.-L. Brylinski J. Dieudonn H. Gillet A.B.Goncharov K. Kato S. Kleiman W. Messing V.V. Schechtman C.S. Seshadri C. Soul J. Tate M. van den Bergh and A.N. Varchenko |
Note: | Springer eBooks |
Contents: | Foreword |
Bibliographie d'Alexander Grothendieck | |
Dieudonne | |
Altman and Kleiman | |
Artin, Tate, and van den Bergh | |
Balaji and Seshadri | |
Beauville | |
Beilinson, Goncharov, Schechtman, and Varchenko | |
Berthelot and Messing | |
Bismut, Gillet, and Soule | |
Bloch and Kato | |
Breen | |
Brylinski | |
ISBN: | 9780817645748 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , K-theory , Functional analysis , Number theory , Algebraic topology |
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Call number: | SPRINGER-2007-9780817644956:ONLINE Show nearby items on shelf |
Title: | An Invitation to Quantum Cohomology [electronic resource] Kontsevichs Formula for Rational Plane Curves |
Author(s): |
Joachim Kock Israel Vainsencher Hyman Bass Joseph Oesterl Alan Weinstein |
Date: | 2007 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
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Note: | This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint ismostly that of enumerativ e geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as astatement about reconstruction for GromovWitten i nvariants, and finally, using generating functions, as a special case of the associativity of the quantum product. Emphasis is given throughout the exposition to examples, heuristicdiscussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry. Some familiarity withbasic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercisesthat complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, a s a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersectiontheory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish t o learn about the subject |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Prologue: Warming Up with Cross | |
ratios, and the Definition of Moduli Space | |
Stable n | |
pointed Curves | |
Stable Maps | |
Enumerative Geometry via Stable Maps | |
GromovWitten Invariants | |
Quantum Cohomology | |
Bibliography | |
Index | |
ISBN: | 9780817644956 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v249 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Geometry , Algebraic topology , Mathematical physics |
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Call number: | SPRINGER-2006-9783834803528:ONLINE Show nearby items on shelf |
Title: | Noncommutative Geometry and Number Theory [electronic resource] : Where Arithmetic meets Geometry and Physics |
Author(s): |
Caterina Consani Matilde Marcolli |
Date: | 2006 |
Publisher: | Wiesbaden : Vieweg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date researchtopics in arithmetic an d noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volumepresent new noncommutative geometry perspecti ves on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local Lfactors of arithmeticvarieties. They also show how arithmetic appears naturally in nonc ommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect |
Note: | Springer eBooks |
ISBN: | 9783834803528 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Aspects of Mathematics, 0179-2156 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2006-9783764376871:ONLINE Show nearby items on shelf |
Title: | C*-algebras and Elliptic Theory [electronic resource] |
Author(s): |
Bogdan Bojarski Alexander S Mishchenko Evgenij V Troitsky Andrzej Weber |
Date: | 2006 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume contains the proceedings of the conference on C*-algebras and Elliptic Theory held in Bedlewo, Poland, in February 2004. It consists of original research papers and expository articles focussing on index theoryand topology of manifolds. T he collection offers a cross-section of significant recent advances in several fields, the main subject being K-theory (of C*-algebras, equivariant K-theory). A number of papers is related to the indextheory of pseudodifferential operators on singular man ifolds (with boundaries, corners) or open manifolds. Further topics are Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others. The wide spectrumof subjects reflects the diverse directions of research emanating from the Atiyah-Singer index theorem. Contributors: B. Bojarski, J. Brodzki, D. Burghelea, A. Connes, J. Eichhorn, T. Fack, S. Haller, Yu.A. Kordyukov, V. Manuilov, V.Nazaikinskii, G.A. Niblo, F. Nicola, I.M. Nikonov, V. Nistor, L. Rodino, A. Savin, V.V. Sharko, G .I. Sharygin, B. Sternin, K. Thomsen, E.V. Troitsky, E. Vasseli, A. Weber |
Note: | Springer eBooks |
Contents: | Preface |
Correspondences and Index | |
Approximation Properties for Discrete Groups | |
A Riemannian Invariant | |
Morse Inequalities for Foliations | |
Index Theory for Generalized Dirac Operators on Open Manifolds | |
Semiclassical Asymptotics and Spectral Gaps for Periodic Magnetic Schrdinger Operators | |
The Group of Unital C* | |
extensions | |
Lefschetz Theory on Manifolds with Singularities | |
Residues and Index for Bisingular Operators | |
Hopf | |
type Cyclic Homology | |
Thom Isomorphism in Gauge | |
Invariant K | |
theory | |
Pseudodifferential Subspaces | |
L2 | |
invariants of Chain Complexes | |
Bundles of | |
ISBN: | 9783764376871 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2006-9783540341970:ONLINE Show nearby items on shelf |
Title: | Operator Algebras [electronic resource] : The Abel Symposium 2004 |
Author(s): |
Ola Bratteli Sergey Neshveyev Christian Skau |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field inmathematics often described as non-commutative geometry (see for example the book Non-Commutative Geometry by the Fields medalist Alain Connes). It has branched out in several subdisciplines and made contact with other subjectslike for example mathematical physics, algebraic topology, geometry, dynamical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in thesubject, which contributed to the award of the first symposium in the series of Abe l Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these subdisciplines |
Note: | Springer eBooks |
Contents: | Interpolation by Projections in C* |
Algebras | |
KMS States and Complex Multiplication (Part II) | |
An Algebraic Description of Boundary Maps Used in Index Theory | |
On Rrdam's Classification of Certain C* | |
Algebras with One Non | |
Trivial Ideal | |
Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C* | |
Algebras of Real Rank Zero | |
Twisted K | |
Theory and Modular Invariants: I Quantum Doubles of Finite Groups | |
The Orbit Structure of Cantor Minimal Z2 | |
Systems | |
Outer Actions of a Group on a Factor | |
Non | |
Separable AF | |
Algebras | |
Central Sequences in C* | |
Algebras and Stron | |
ISBN: | 9783540341970 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia : v1 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Differentiable dynamical systems , Functional analysis , Operator theory |
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Call number: | SPRINGER-2006-9783540285175:ONLINE Show nearby items on shelf |
Title: | Operator Algebras [electronic resource] : Theory of C-Algebras and von Neumann Algebras |
Author(s): |
Bruce Blackadar |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is the most comprehensive treatment available of the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity andexactness, crossed product s, classification of injective factors, K-theory, finiteness, stable rank, and quasidiagonality. The presentation concentrates on carefully and precisely explaining the main features of each part of the theoryof operator algebras most important arguments are at least outlined, and many are presented in full detail, so the volume is much more than a mere survey |
Note: | Springer eBooks |
ISBN: | 9783540285175 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v122 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory , Functional analysis , Operator theory , Geometry , Topology , Mathematical physics |
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Call number: | SPRINGER-2006-9783540279914:ONLINE Show nearby items on shelf |
Title: | Idempotent Matrices over Complex Group Algebras [electronic resource] |
Author(s): |
Ioannis Emmanouil |
Date: | 2006 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. The relevant questions studied in thisbook for general groups are motivated by specific examples. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis. The book can serve as an introduction to this lively research area.The pace is suitable for independent study a nd the level of the presentation not very demanding. The exercises at the end of each chapter form an essential part of the book |
Note: | Springer eBooks |
Contents: | Introduction |
Motivating Examples | |
Reduction to Positive Characteristic | |
A Homological Approach | |
Completions of CG | |
Appendices: Tools from Commutative Algebra | |
Discrete Ring | |
valued Integrals | |
Frobenius' Density Theorem | |
Homological Techniques | |
Comparison of Projections | |
ISBN: | 9783540279914 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , K-theory , Functional analysis |
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Call number: | SPRINGER-2006-9780817644673:ONLINE Show nearby items on shelf |
Title: | The Unity of Mathematics [electronic resource] In Honor of the Ninetieth Birthday of I.M. Gelfand |
Author(s): |
Pavel Etingof Vladimir Retakh I. M Singer |
Date: | 2006 |
Publisher: | Boston, MA : Birkhuser Boston |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Springer eBooks |
ISBN: | 9780817644673 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v244 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Group theory , K-theory , Topological Groups , Geometry , Mathematical physics |
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Call number: | SPRINGER-2005-9783540315223:ONLINE Show nearby items on shelf |
Title: | Geometric and Topological Methods for Quantum Field Theory [electronic resource] |
Author(s): |
Hernn Ocampo Sylvie Paycha Andrs Vargas |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is byChristine Lescop on knot inv ariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of RaimarWulkenhaar on Euclidean quantum field theory from a sta tistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on stringcompactification with unbroken supersymmetry. The authors show that this requ irement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theoryproof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommuta tive geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start withintroductory material before presenting more advanced results. Each chapter is self-contained and can be read independently |
Note: | Springer eBooks |
Contents: | Knot Invariants and Configuration Space Integrals (Christine Lescop) |
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) | |
Introduction to String Compactification (Anamaria Font, Stefan Theisen) | |
Index Theorems and Noncommutative Topology (Thierry Fack) | |
ISBN: | 9783540315223 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v668 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Global differential geometry , Cell aggregation Mathematics , Mathematical physics , Quantum theory |
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Call number: | SPRINGER-2005-9783540278559:ONLINE Show nearby items on shelf |
Title: | Handbook of K-Theory [electronic resource] |
Author(s): |
Eric M Friedlander Daniel R Grayson |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historicalbackground some presen t previously unpublished results, whereas some present the first expository account of a topic many discuss future directions as well as open problems. The overall intent of this handbook is to offer theinterested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for students wishing to obtain an overview of K-theory and formathematicians interested in pursuing challenges in this rapidly expanding field |
Note: | Springer eBooks |
Contents: | Part I: Foundations and Computations: Deloopings in Algebraic K |
theory | |
The Motivic Spectral Sequence | |
K | |
theory of truncated polynomial algebras | |
Bott Periodicity in Topological, Algebraic and Hermitian K | |
theory | |
Algebraic K | |
theory of Rings and Integers in Local and Global Fields. Part II: K | |
theory and Algebraic Geometry: Motivic Cohomology, K | |
theory and topological cyclic Homology | |
K | |
theory and Intersection Theory | |
Regulators | |
Algebraic K | |
theory, Algebraic Cycles and Arithmetic Geometry | |
Mixed Motives. Part III: K | |
theory and Geometric Topology: Witt Groups | |
K | |
theory and Geo | |
ISBN: | 9783540278559 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , K-theory , Number theory , Algebraic topology |
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Call number: | SPRINGER-2005-9783540264743:ONLINE Show nearby items on shelf |
Title: | Basic Notions of Algebra [electronic resource] |
Author(s): |
Igor R Shafarevich |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | From the reviews: This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights... Zentralblatt fr Mathematik undIhre Grenzgebiete, 1991 ... which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ...Furthermore, at the end of the book, there are so me Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraicgeometer. Nieuw Archief voor Wiskunde, 1992 ... There are few proofs in full , but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly acrossthe whole spectrum of algebra.... The challenge to Ezekiel, Can these bones live? is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book -which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers... The Mathematical Gazette, 1991 ... According to the preface, the book is addressed tostudents of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impre ssion of the spirit of algebra and its place in mathematics. I thinkthat this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions - all will read this exceptional book with great p leasure and benefit. Zeitschrift frKristallographie, 1991 |
Note: | Springer eBooks |
Contents: | Preface |
1 What is Algebra? | |
2 Fields | |
3 Commutative Rings | |
4 Homomorphisms and Ideals | |
5 Modules | |
6 Algebraic Aspects of Dimension | |
7 The Algebraic View of Infinitesimal Notions | |
8 Noncommutative Rings | |
9 Modules and Noncommutative Rings | |
10 Semisimple Modules and Rings | |
11 Division Algebras of Finite Rank | |
12 The Notion of a Group | |
13 Examples of Groups: Finite Groups | |
14 Examples of Groups: Infinite Discrete Groups | |
15 Examples of Groups : Lie Groups and Algebraic Groups | |
16 General Results of Group Theory | |
17 Group Representations | |
18 Some Applications of | |
ISBN: | 9783540264743 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v11 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Topological Groups |
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Call number: | SPRINGER-2005-9783540263708:ONLINE Show nearby items on shelf |
Title: | Ideals and Reality [electronic resource] : Projective Modules and Number of Generators of Ideals |
Author(s): |
Friedrich Ischebeck Ravi A Rao |
Date: | 2005 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre'sconjecture. The central topi c of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1)$ hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratnski.The book gives a comprehensive introduction to bas ic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of usingthese tools. At the same time, it also serves as a valuable reference for t he research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix ofclassical algebraic K-theory and complete intersection techniques, making connections with the fa mous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in aform due to Vaserstein is included. Important subsidiary results appear in the copious exercises. Even this advanced m aterial, presented comprehensively, keeps in mind the young student as potential reader besides the specialists ofthe subject |
Note: | Springer eBooks |
ISBN: | 9783540263708 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2004-9783662064443:ONLINE Show nearby items on shelf |
Title: | Cyclic Homology in Non-Commutative Geometry |
Author(s): |
Joachim Cuntz |
Date: | 2004 |
Size: | 1 online resource (137 p.) |
Note: | 10.1007/978-3-662-06444-3 |
Contents: | I. Cyclic Theory, Bivariant K-Theory and the Bivariant Chern-Connes Character by J. Cuntz: 1. Cyclic Theory 2. Cyclic Theory for Locally Convex Algebras 3. Bivariant K-Theory 4. Infinite-Dimensional Cyclic Theories A. Locally Convex |
Algebras B. Standard Extensions -- II. Noncommutative Geometry, the Transverse Signature Operator, and Hopf Algebras (after A. Connes and H. Moscovici) by G. Skandalis: 1. Preliminaries 2. The Local Index Formula 3. The Diff-Invariant | |
Signature Operator 4. The 'Transverse' Hopf Algebra -- III. Cyclic Homology by B. Tsygan: 1. Introduction 2. Hochschild and Cyclic Homology of Algebras 3. The Cyclic Complex C^{lambda}_{bullet} 4. Non-Commutative Differential Calculus | |
5. Cyclic Objects 6. Examples 7. Index Theorems 8. Riemann-Roch Theorem for D-Modules | |
ISBN: | 9783662064443 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Encyclopaedia of Mathematical Sciences, Operator Algebras and Non-Commutative Geometry II: 121 |
Keywords: | Mathematics , Operator theory , Algebraic topology , Physics , Mathematics , Operator Theory , Theoretical, Mathematical and Computational Physics , Algebraic Topology |
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Call number: | SPRINGER-2004-9783662062807:ONLINE Show nearby items on shelf |
Title: | Cohomology of Finite Groups |
Author(s): |
Alejandro Adem |
Date: | 2004 |
Edition: | Second Edition |
Size: | 1 online resource (324 p.) |
Note: | 10.1007/978-3-662-06280-7 |
Contents: | I. Group Extensions, Simple Algebras and Cohomology -- II. Classifying Spaces and Group Cohomology -- III. Invariants and Cohomology of Groups -- IV. Spectral Sequences and Detection Theorems -- V. G-Complexes and Equivariant |
Cohomology -- VI. The Cohomology of the Symmetric Groups -- VII. Finite Groups of Lie Type -- VIII. Cohomology of Sporadic Simple Groups -- IX. The Plus Construction and Applications -- X. The Schur Subgroup of the Brauer Group -- | |
References | |
ISBN: | 9783662062807 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 309 |
Keywords: | Mathematics , Algebra , Group theory , K-theory , Algebraic topology , Mathematics , Algebra , Group Theory and Generalizations , Algebraic Topology , K-Theory |
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Call number: | SPRINGER-2004-9783540397021:ONLINE Show nearby items on shelf |
Title: | Noncommutative Geometry Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 3-9, 2000 |
Author(s): |
Alain Connes |
Date: | 2004 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource (356 p.) |
Note: | 10.1007/b94118 |
Contents: | Cyclic Cohomology, Noncommutative Geometry and Quantum Group Symmetries -- Cyclic Theory and the Bivariant Chern-Connes Character -- Group C*-Algebras and K-Theory -- Geometric and Analytic Properties of Groups -- More Lectures on |
Algebraic Quantum Field Theory | |
ISBN: | 9783540397021 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics, Fondazione C.I.M.E., Firenze: 1831 |
Keywords: | Mathematics , Functional analysis , Global analysis (Mathematics) , Manifolds (Mathematics) , Gravitation , Quantum physics , Mathematics , Global Analysis and Analysis on Manifolds , Functional Analysis , Quantum Physics , Classical and Quantum Gravitation, Relativity Theory |
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Call number: | SPRINGER-2004-9783034878630:ONLINE Show nearby items on shelf |
Title: | Categorical Decomposition Techniques in Algebraic Topology International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 |
Author(s): | |
Date: | 2004 |
Size: | 1 online resource (304 p.) |
Note: | 10.1007/978-3-0348-7863-0 |
Contents: | The functor T and the cohomology of mapping spaces -- On Morava K-theories of an S-arithmetic Group -- Ext groups for the composition of functors -- Homotopy operations and rational homotopy type -- The loop homology algebra of |
spheres and projective spaces -- On braid groups, free groups, and the loop space Of the 2-sphere -- The K-completion of E6 -- The Homotopy of L2V(1) for the Prime 3 -- Spherical Space Forms — Homotopy Types and Self-Equivalences -- | |
The Homotopy Type of Two-Regular K-Theory -- Strict model structures for pro-categories -- L-s categories of simply-connected compact simple lie groups Of low rank -- The mccord model for the tensor product of a space And a commutative | |
ring spectrum -- Spaces of multiplicative maps between Highly structured ring spectra -- Colimits, stanley-reisner algebras, and loop spaces -- Maps to spaces in the genus of infinite quaternionic Projective space | |
ISBN: | 9783034878630 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 215 |
Keywords: | Mathematics , Category theory (Mathematics) , Homological algebra , Algebraic topology , Mathematics , Algebraic Topology , Category Theory, Homological Algebra |
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Call number: | SPRINGER-2002-9789401003452:ONLINE Show nearby items on shelf |
Title: | Dynamics and Randomness |
Author(s): | |
Date: | 2002 |
Size: | 1 online resource (278 p.) |
Note: | 10.1007/978-94-010-0345-2 |
Contents: | Dimension-Like Characteristics of Invariant Sets in Dynamical Systems. -- Positive K-Theory and Symbolic Dynamics. -- Combinatorial and Dynamical Study of Substitutions around the Theorem of Cobham. -- Irreducibility, Homoclinic |
Points and Adjoint Actions of Algebraic Zd-Actions of Rank One. -- Old and New Tools in the Theory of Filtrations. -- Information Compression and Retention in Dynamical Processes. -- Unique Equilibrium States. -- Poincaré Inequalities | |
and Spectral Gap, Concentration Phenomenon for g-Measures | |
ISBN: | 9789401003452 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Nonlinear Phenomena and Complex Systems: 7 |
Keywords: | Mathematics , Coding theory , Computer science , Probabilities , Statistical physics , Dynamical systems , Mathematics , Probability Theory and Stochastic Processes , Coding and Information Theory , Discrete Mathematics in Computer Science , Statistical Physics, Dynamical Systems and Complexity |
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Call number: | SPRINGER-2002-9783662049679:ONLINE Show nearby items on shelf |
Title: | Galois Theory of p-Extensions |
Author(s): |
Helmut Koch |
Date: | 2002 |
Size: | 1 online resource (191 p.) |
Note: | 10.1007/978-3-662-04967-9 |
Contents: | 1. Profinite Groups -- 2. Galois Theory of Infinite Algebraic Extensions -- 3. Cohomology of Profinite Groups -- 4. Free pro-p Groups -- 5. Cohomological Dimension -- 6. Presentation of pro-p Groups -- 7. Group Algebras of pro-p |
Groups -- 8. Results from Algebraic Number Theory -- 9. The Maximal p-Extension -- 10. Local Fields of Finite Type -- 11. Global Fields of Finite Type -- 12. On p-Class Groups and p-Class Field Towers -- 13. The Cohomological Dimension | |
of GS -- References -- Notation -- Postscript -- Additional References -- Author Index | |
ISBN: | 9783662049679 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Group theory , K-theory , Mathematics , K-Theory , Group Theory and Generalizations |
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Call number: | SPRINGER-2002-9783662046876:ONLINE Show nearby items on shelf |
Title: | L2-Invariants: Theory and Applications to Geometry and K-Theory |
Author(s): |
Wolfgang Lück |
Date: | 2002 |
Size: | 1 online resource (595 p.) |
Note: | 10.1007/978-3-662-04687-6 |
Contents: | 0. Introduction -- 1. L2-Betti Numbers -- 2. Novikov-Shubin Invariants -- 3. L2-Torsion -- 4. L2-Invariants of 3-Manifolds -- 5. L2-Invariants of Symmetric Spaces -- 6. L2-Invariants for General Spaces with Group Action -- 7. |
Applications to Groups -- 8. The Algebra of Affiliated Operators -- 9. Middle Algebraic K-Theory and L-Theory of von Neumann Algebras -- 10. The Atiyah Conjecture -- 11. The Singer Conjecture -- 12. The Zero-in-the-Spectrum Conjecture | |
-- 13. The Approximation Conjecture and the Determinant Conjecture -- 14. L2-Invariants and the Simplicial Volume -- 15. Survey on Other Topics Related to L2-Invariants -- 16. Solutions of the Exercises -- References -- Notation | |
ISBN: | 9783662046876 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics: 44 |
Keywords: | Mathematics , K-theory , Geometry , Topology , Algebraic topology , Mathematics , Algebraic Topology , Geometry , K-Theory , Topology |
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Call number: | SPRINGER-2002-9783540362050:ONLINE Show nearby items on shelf |
Title: | Iwahori-Hecke Algebras and their Representation Theory Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 28 - July 6, 1999 |
Author(s): |
Ivan Cherednik |
Date: | 2002 |
Size: | 1 online resource (114 p.) |
Note: | 10.1007/b10326 |
Contents: | Preface -- I. Cherednik and Ya. Markov: Hankel transform via double Hecke algebra -- R. Howe: Affine-like Hecke algebras and p-adic representation theory -- G. Lusztig: Notes on affine Hecke algebras |
ISBN: | 9783540362050 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics, Fondazione C.I.M.E., Firenze: 1804 |
Keywords: | Mathematics , Group theory , K-theory , Operator theory , Mathematics , Group Theory and Generalizations , K-Theory , Operator Theory |
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Call number: | SPRINGER-2002-9783034882071:ONLINE Show nearby items on shelf |
Title: | Algebraic K-Groups as Galois Modules |
Author(s): |
Victor P Snaith |
Date: | 2002 |
Size: | 1 online resource (309 p.) |
Note: | 10.1007/978-3-0348-8207-1 |
Contents: | 1 Galois Actions and L-values -- 1.1 Analytic prerequisites -- 1.2 The Lichtenbaum conjecture -- 1.3 Examples of Galois structure invariants -- 2 K-groups and Class-groups -- 2.1 Low-dimensional algebraic K-theory -- 2.2 Perfect |
complexes -- 2.3 Nearly perfect complexes -- 2.4 Higher-dimensional algebraic K-theory -- 2.5 Describing the class-group by representations -- 3 Higher K-theory of Local Fields -- 3.1 Local fundamental classes and K-groups -- 3.2 The | |
higher K-theory invariants ?s(L/K,2) -- 3.3 Two-dimensional thoughts -- 4 Positive Characteristic -- 4.1 ?1(L/K,2) in the tame case -- 4.2 $$ Ext_{Z[G(L/K)]}^2(F_{{v^d}}^*,F_{{v^{2d}}}^*) $$ -- 4.3 Connections with motivic complexes -- | |
5 Higher K-theory of Algebraic Integers -- 5.1 Positive étale cohomology -- 5.2 The invariant ?n(N/K,3) -- 5.3 A closer look at ?1(L/K,3) -- 5.4 Comparing the two definitions -- 5.5 Some calculations -- 5.6 Lifted Galois invariants -- | |
6 The Wiles unit -- 6.1 The Iwasawa polynomial -- 6.2 p-adic L-functions -- 6.3 Determinants and the Wiles unit -- 6.4 Modular forms with coefficients in ?[G] -- 7 Annihilators -- 7.1K0(Z[G], Q) and annihilator relations -- 7.2 | |
Conjectures of Brumer, Coates and Sinnott -- 7.3 The radical of the Stickelberger ideal | |
ISBN: | 9783034882071 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Progress in Mathematics : 206 |
Keywords: | Mathematics , Algebraic geometry , Number theory , Mathematics , Number Theory , Algebraic Geometry |
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Call number: | SPRINGER-2002-9783034881876:ONLINE Show nearby items on shelf |
Title: | Introduction to the Baum-Connes Conjecture |
Author(s): |
Alain Valette |
Date: | 2002 |
Size: | 1 online resource (104 p.) |
Note: | 10.1007/978-3-0348-8187-6 |
Contents: | 1 Idempotents in Group Algebras -- 2 The Baum-Connes Conjecture -- 3K-theory for (Group) C*-algebras -- 4 Classifying Spaces andK-homology -- 5 EquivariantKK-theory -- 6 The Analytical Assembly Map -- 7 Some Examples of the Assembly |
Map -- 8 Property (RD) -- 9 The Dirac-dual Dirac Method -- 10 Lafforgue’sKKBan Theory -- G. Mislin: On the Classifying Space for Proper Actions -- A.1 The topologist’s model -- A.2 The analyst’s model -- A.4 Spectra | |
ISBN: | 9783034881876 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Group theory , K-theory , Topological groups , Lie groups , Geometry , Mathematics , Algebra , Geometry , K-Theory , Topological Groups, Lie Groups , Group Theory and Generalizations |
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Call number: | SPRINGER-2002-9780387224893:ONLINE Show nearby items on shelf |
Title: | Algebraic Topology from a Homotopical Viewpoint |
Author(s): |
Marcelo Aguilar |
Date: | 2002 |
Size: | 1 online resource (479 p.) |
Note: | 10.1007/b97586 |
Contents: | Function Spaces -- Connectedness and Algebraic Invariants -- Homotopy groups -- Homotopy Extension and Lifting Properties -- CW-Complexes and Homology -- Homotopy Properties of CW-Complexes -- Cohomology Groups and Related Topics -- |
Vector Bundles -- K-Theory -- Adams Operations and Applications -- Relations Between Cohomology and Vector Bundles -- Cohomology Theories and Brown Representability | |
ISBN: | 9780387224893 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Topology , Algebraic topology , Mathematics , Topology , Algebraic Topology |
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Call number: | SPRINGER-2001-9789401008525:ONLINE Show nearby items on shelf |
Title: | Progress in String Theory and M-Theory |
Author(s): | |
Date: | 2001 |
Size: | 1 online resource (417 p.) |
Note: | 10.1007/978-94-010-0852-5 |
Contents: | Lectures -- Scales of String/M Theory -- On the Heterotic/F-Theory Duality in Eight Dimensions -- Large N Field Theories, String Theory and Gravity -- Black Holes and the Phases of Brane Thermodynamics -- Non-BPS-D-Brane Systems -- |
Non-BPS States and Branes in String Theory -- Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces -- Brane Theory Solitons -- Gong Show -- D-Branestrahlung -- Strings on BTZ Black Holes -- A Note on | |
non-supersymmetric Open-String Orbifolds with a quantised Bab -- On the Non-Abelian Born-Infeld Action -- AdS3 asymptotic (super) Symmetries -- Anomalous couplings of Non-BPS D-Branes -- Fron a Conformal Anomaly to a Theory of | |
Tensionless Strings? -- Comments on non-supersymmetric type I vacua -- S-Matrices for Planckian Scattering -- K-Theory and D-Branes on NON-Commutative Rori -- Generalized Calibrations -- Aspects of Heterotic/M-Theory Duality in D=3 -- | |
Gauge Theory scattering from the ADS/CFT correspondence -- Flat Connections for Yang-Mills Theories on the 3-Torus -- From Topological Field Theories to Covariant Matrix Strings -- Field Theory Duals from (Non)-Crital Type 0 Strings -- | |
Duality and Selfduality of Chiral Boson Fields in various Dimensions -- Anti-de Sitter Fragmentation -- On ADS3 String Theory -- Spectrum of D=11 Supergravity on ADS2 × S2 × T7 -- Discrete U-duality groups -- Supersymmetric Worldvolume | |
Solitons -- WZ Couplings of D-Branes and O-Planes -- Holography for Coset Spaces -- List of Speakers -- List of Participants | |
ISBN: | 9789401008525 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | NATO Science Series, Series C: Mathematical and Physical Sciences: 564 |
Keywords: | Physics , Nuclear physics , Heavy ions , Hadrons , Elementary particles (Physics) , Quantum field theory , Physics , Elementary Particles, Quantum Field Theory , Nuclear Physics, Heavy Ions, Hadrons , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2001-9783662045763:ONLINE Show nearby items on shelf |
Title: | Weil Conjectures, Perverse Sheaves and l’adic Fourier Transform |
Author(s): |
Reinhardt Kiehl |
Date: | 2001 |
Size: | 1 online resource (375 p.) |
Note: | 10.1007/978-3-662-04576-3 |
Contents: | I. The General Weil Conjectures (Deligne’s Theory of Weights) -- II. The Formalism of Derived Categories -- III. Perverse Sheaves -- IV. Lefschetz Theory and the Brylinski—Radon Transform -- V. Trigonometric Sums -- VI. The Springer |
Representations -- B. Bertini Theorem for Etale Sheaves -- C. Kummer Extensions -- D. Finiteness Theorems | |
ISBN: | 9783662045763 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics: 42 |
Keywords: | Mathematics , Algebraic geometry , Group theory , K-theory , Mathematics , Algebraic Geometry , Group Theory and Generalizations , K-Theory |
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