Volume 726 2008

Basic Bundle Theory and K-Cohomology Invariants

With contributions by Siegfried Echterhoff, Stefan Fredenhagen and Bernhard Krötz

Authors:

ISBN: 978-3-540-74955-4 (Print) 978-3-540-74956-1 (Online)

Table of contents (27 chapters)

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  1. Front Matter

    Pages I-XV

  2. Physical Background to the K-Theory Classification of D-Branes: Introduction and References

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 1-6

      Physical Background to the K-Theory Classification of D-Branes: Introduction and References

  3. Bundles over a Space and Modules over an Algebra

    1. Front Matter

      Pages 7-8

    2. No Access

      Book Chapter

      Pages 9-22

      Generalities on Bundles and Categories

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      Book Chapter

      Pages 23-34

      Vector Bundles

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      Book Chapter

      Pages 35-44

      Relation Between Vector Bundles, Projective Modules, and Idempotents

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      Book Chapter

      Pages 45-54

      K-Theory of Vector Bundles, of Modules, and of Idempotents

    6. No Access

      Book Chapter

      Pages 55-62

      Principal Bundles and Sections of Fibre Bundles: Reduction of the Structure and the Gauge Group I

  4. Homotopy Classification of Bundles and Cohomology: Classifying Spaces

    1. Front Matter

      Pages 63-64

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      Book Chapter

      Pages 65-74

      Homotopy Classes of Maps and the Homotopy Groups

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      Book Chapter

      Pages 75-81

      The Milnor Construction: Homotopy Classification of Principal Bundles

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      Book Chapter

      Pages 83-96

      Fibrations and Bundles: Gauge Group II

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      Book Chapter

      Pages 97-109

      Cohomology Classes as Homotopy Classes: CW-Complexes

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      Book Chapter

      Pages 111-125

      Basic Characteristic Classes

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      Book Chapter

      Pages 127-135

      Characteristic Classes of Manifolds

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      Book Chapter

      Pages 137-145

      Spin Structures

  5. Versions of K-Theory and Bott Periodicity

    1. Front Matter

      Pages 146-147

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      Book Chapter

      Pages 149-161

      G-Spaces, G-Bundles, and G-Vector Bundles

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      Book Chapter

      Pages 163-173

      Equivariant K-Theory Functor KG : Periodicity, Thom Isomorphism, Localization, and Completion

    4. No Access

      Book Chapter

      Pages 175-188

      Bott Periodicity Maps and Clifford Algebras

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      Book Chapter

      Pages 189-201

      Gram–Schmidt Process, Iwasawa Decomposition, and Reduction of Structure in Principal Bundles

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      Book Chapter

      Pages 203-226

      Topological Algebras: G-Equivariance and KK-Theory

  6. Algebra Bundles: Twisted K-Theory

    1. Front Matter

      Pages 227-228

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      Book Chapter

      Pages 229-239

      Isomorphism Classification of Operator Algebra Bundles

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      Book Chapter

      Pages 241-249

      Brauer Group of Matrix Algebra Bundles and K-Groups

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