Basic Bundle Theory and K-Cohomology Invariants

Naslovnica
Springer 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.

 

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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
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