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SPIRES-BOOKS: FIND KEYWORD K-THEORY *END*INIT* use /tmp/qspiwww.webspi1/29120.7 QRY 131.225.70.96 . find keyword k-theory ( in books using www Cover
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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 A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It isa natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to theproperties and computations of A1-homotopy sheaves, A1-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties
Note:Springer eBooks
Contents:1 Introduction
2 Unramified sheaves and strongly A1
invariant sheaves
3 Unramified Milnor
Witt K
theories
4 Geometric versus canonical transfers
5 The Rost
Schmid complex of a strongly A1
invariant sheaf
6 A1
homotopy sheaves and A1
homology sheaves
7 A1
coverings
8 A1
homotopy and algebraic vector bundles
9 The affine B.G. property for the linear groups and the Grassmanian
ISBN:9783642295140
Series:e-books
Series:SpringerLink (Online service)
Series:Lecture Notes in Mathematics, 0075-8434 : v2052
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Geometry, algebraic , K-theory , Algebraic topology
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Call number:SPRINGER-2012-9783034802574: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
Note:Springer 2013 e-book collections
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
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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
Note:Springer e-book platform
Note:Springer 2013 e-book collections
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
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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
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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
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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
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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
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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
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Note:Springer 2013 e-book collections
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
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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
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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
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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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