Basic Bundle Theory and K-Cohomology InvariantsSpringer Science & Business Media, 18. pro 2007. - Broj stranica: 340 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 fundamental theme, emphasized in the 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, comes from quantum field theory, especially string theory, where topological invariants play an important role. |
Sadržaj
Introduction and References | 1 |
Part I Bundles over a Space and Modules over an Algebra | 7 |
Generalities on Bundles and Categories | 9 |
Vector Bundles | 23 |
Relation Between Vector Bundles Projective Modules and Idempotents | 35 |
KTheory of Vector Bundles of Modules and of Idempotents | 45 |
Reduction of the Structure and the Gauge Group I | 55 |
Classifying Spaces | 63 |
GSpaces GBundles and GVector Bundles | 148 |
Periodicity Thom Isomorphism Localization and Completion | 163 |
Bott Periodicity Maps and Clifford Algebras | 174 |
GramSchmidt Process Iwasawa Decomposition and Reduction of Structure | 189 |
GEquivariance and KKTheory | 203 |
Twisted KTheory | 227 |
Isomorphism Classification of Operator Algebra Bundles | 229 |
Brauer Group of Matrix Algebra Bundles and KGroups | 240 |
Homotopy Classes of Maps and the Homotopy Groups | 65 |
Homotopy Classification of Principal Bundles | 75 |
Gauge Group II | 82 |
CWComplexes | 97 |
Basic Characteristic Classes | 111 |
Characteristic Classes of Manifolds | 126 |
Spin Structures | 137 |
Part III Versions of KTheory and Bott Periodicity | 146 |
Analytic Definition of Twisted KTheory | 251 |
The AtiyahHirzebruch Spectral Sequence in KTheory | 254 |
Twisted Equivariant KTheory and the Verlinde Algebra | 265 |
Part V Gerbes and the Three Dimensional Integral Cohomology Classes | 275 |
Bundle Gerbes | 277 |
Category Objects and Groupoid Gerbes | 287 |
Stacks and Gerbes | 303 |
Ostala izdanja - Prikaži sve
Basic Bundle Theory and K-Cohomology Invariants Dale Husemöller,Michael Joachim,Branislav Jurco,Martin Schottenloher Ograničeni pregled - 2007 |
Basic Bundle Theory and K-Cohomology Invariants Dale Husemöller,Michael JOACHIM,Branislav Jurco,Martin Schottenloher Pregled nije dostupan - 2010 |
Basic Bundle Theory and K-Cohomology Invariants Dale Husemöller,Michael JOACHIM,Branislav Jurco,Martin Schottenloher Pregled nije dostupan - 2009 |
Uobičajeni izrazi i fraze
abelian group adjoint algebra bundles Atiyah basic bijection bundle gerbes bundle of vector C*-algebra Chap characteristic class Chern classes classifying space cofibre cohomology complex vector bundle composition cross sections D-branes decomposition defined Definition Let denote elements exact sequence Example extension fibration fibre bundle fibre product formula function functor G-bundle G-equivariant G-space G-vector given GL(n Grothendieck group G groupoid Hilbert space homology homotopy classes homotopy equivalence Husemöller idempotents inclusion induced inverse isomorphism classes K-groups Lie group line bundle linear locally convex manifold map f map ƒ matrix algebra bundles Milnor modules Notation Let numbers open set operator algebra bundles orientation pair phism pointed space principal bundle product bundle Proof Proposition Let quotient real vector bundle relation Remark Let resp restriction ring sheaf SO(n spectral sequence Stiefel-Whitney Stiefel-Whitney class structure subgroup subset subspace theorem theory topological group twisted K-theory vector space Whitney sum