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Fibre Bundles

  • Textbook
  • © 1994

Overview

Authors:
  1. Dale Husemoller

    1. Department of Mathematics, Haverford College, Haverford, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 20)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xix
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  2. Preliminaries on Homotopy Theory

    1. Preliminaries on Homotopy Theory

      • Dale Husemoller
      Pages 1-8

  3. The General Theory of Fibre Bundles

    1. Front Matter

      Pages 9-9
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    2. Generalities on Bundles

      • Dale Husemoller
      Pages 11-23

    3. Vector Bundles

      • Dale Husemoller
      Pages 24-39

    4. General Fibre Bundles

      • Dale Husemoller
      Pages 40-60

    5. Local Coordinate Description of Fibre Bundles

      • Dale Husemoller
      Pages 61-72

    6. Change of Structure Group in Fibre Bundles

      • Dale Husemoller
      Pages 73-78

    7. The Gauge Group of a Principal Bundle

      • Dale Husemoller
      Pages 79-86

    8. Calculations Involving the Classical Groups

      • Dale Husemoller
      Pages 87-107

  4. Elements of K-Theory

    1. Front Matter

      Pages 109-109
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    2. Stability Properties of Vector Bundles

      • Dale Husemoller
      Pages 111-121

    3. Relative K-Theory

      • Dale Husemoller
      Pages 122-139

    4. Bott Periodicity in the Complex Case

      • Dale Husemoller
      Pages 140-150

    5. Clifford Algebras

      • Dale Husemoller
      Pages 151-170

    6. The Adams Operations and Representations

      • Dale Husemoller
      Pages 171-188

    7. Representation Rings of Classical Groups

      • Dale Husemoller
      Pages 189-209

    8. The Hopf Invariant

      • Dale Husemoller
      Pages 210-216

    9. Vector Fields on the Sphere

      • Dale Husemoller
      Pages 217-242

  5. Characteristic Classes

    1. Front Matter

      Pages 243-243
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Keywords

About this book

Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles.

Authors and Affiliations

  • Department of Mathematics, Haverford College, Haverford, USA

    Dale Husemoller

Bibliographic Information

  • Book Title: Fibre Bundles

  • Authors: Dale Husemoller

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-2261-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1994

  • Hardcover ISBN: 978-0-387-94087-8Published: 09 December 1993

  • Softcover ISBN: 978-1-4757-2263-5Published: 14 December 2012

  • eBook ISBN: 978-1-4757-2261-1Published: 09 March 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XX, 356

  • Topics: Algebraic Topology, Topology

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