Basic Bundle Theory and K-Cohomology Invariants

With contributions by Siegfried Echterhoff, Stefan Fredenhagen and Bernhard Krötz

  • D. Husemöller
  • M. Joachim
  • B. Jurčo
  • M. Schottenloher
Part of the Lecture Notes in Physics book series (LNP, volume 726)

Table of contents

  1. Front Matter
    Pages I-XV
  2. 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. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 9-22
    3. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 23-34
    4. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 35-44
    5. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 45-54
    6. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 55-62
  4. Homotopy Classification of Bundles and Cohomology: Classifying Spaces

    1. Front Matter
      Pages 63-64
    2. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 65-74
    3. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 75-81
    4. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 83-96
    5. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 97-109
    6. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 111-125
    7. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 127-135
    8. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 137-145
  5. Versions of K-Theory and Bott Periodicity

    1. Front Matter
      Pages 146-147
    2. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 149-161
    3. D. Husemöller, M. Joachim, B. Jurčo, M. Schottenloher
      Pages 163-173

About this book

Introduction

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.

Keywords

Cohomology D-branes K-Cohomology algebra category theory fibre bundles mathematical physics ring theory topological invariant

Authors and affiliations

  • D. Husemöller
    • 1
  • M. Joachim
    • 2
  • B. Jurčo
    • 3
  • M. Schottenloher
    • 4
  1. 1.MPI für Mathematik53111 BonnGermany
  2. 2.Mathematisches InstitutUniversität MünsterGermany
  3. 3.MPI für Mathematik53111 BonnGermany
  4. 4.Mathematisches InstitutUniversität MünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74956-1
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-74955-4
  • Online ISBN 978-3-540-74956-1
  • Series Print ISSN 0075-8450