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Topology and Analysis

The Atiyah-Singer Index Formula and Gauge-Theoretic Physics

  • B. Booss
  • D. D. Bleecker

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Operators with Index

    1. B. Booss, D. D. Bleecker
      Pages 1-5
    2. B. Booss, D. D. Bleecker
      Pages 5-12
    3. B. Booss, D. D. Bleecker
      Pages 12-25
    4. B. Booss, D. D. Bleecker
      Pages 26-34
    5. B. Booss, D. D. Bleecker
      Pages 34-47
    6. B. Booss, D. D. Bleecker
      Pages 47-60
    7. B. Booss, D. D. Bleecker
      Pages 60-78
    8. B. Booss, D. D. Bleecker
      Pages 79-85
    9. B. Booss, D. D. Bleecker
      Pages 85-102
  3. Analysis on Manifolds

    1. B. Booss, D. D. Bleecker
      Pages 103-125
    2. B. Booss, D. D. Bleecker
      Pages 126-143
    3. B. Booss, D. D. Bleecker
      Pages 144-172
    4. B. Booss, D. D. Bleecker
      Pages 172-181
    5. B. Booss, D. D. Bleecker
      Pages 182-188
    6. B. Booss, D. D. Bleecker
      Pages 189-198
    7. B. Booss, D. D. Bleecker
      Pages 208-217
  4. The Atiyah-Singer Index Formula

    1. B. Booss, D. D. Bleecker
      Pages 218-246
    2. B. Booss, D. D. Bleecker
      Pages 246-256
    3. B. Booss, D. D. Bleecker
      Pages 256-269
    4. B. Booss, D. D. Bleecker
      Pages 269-304
  5. The Index Formula and Gauge-Theoretical Physics

    1. B. Booss, D. D. Bleecker
      Pages 305-331
    2. B. Booss, D. D. Bleecker
      Pages 331-358
    3. B. Booss, D. D. Bleecker
      Pages 359-401
  6. Back Matter
    Pages 402-451

About this book

Introduction

The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi­ ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe­ matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ­ ent mathematical approaches, and must have experience with their inter­ connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela­ tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many­ facetted and always new presentations of the material by M. F.

Keywords

Atiyah-Singersche Indexformel Chern class Finite Microsoft Access Riemann surface Vector field analysis on manifolds character differential operator function instanton integral proof topology variable

Authors and affiliations

  • B. Booss
    • 1
  • D. D. Bleecker
    • 2
  1. 1.IMFUFARoskilde UniversitetscenterRoskildeDenmark
  2. 2.Department of MathematicsUniversity of HawaiiHonoluluUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0627-6
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96112-5
  • Online ISBN 978-1-4684-0627-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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