Topology analysis

© 1985

Topology and Analysis

The Atiyah-Singer Index Formula and Gauge-Theoretic Physics

• Authors
• [view affiliations]

• B.Booss
• D.D.Bleecker

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• 27 Citations
• 3 Mentions
• 27k Downloads

Part of the Universitext book series [UTX]

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• Chapters Table of contents [24 chapters]
• About About this book

Table of contents

Page 1 Navigate to page number of 2

1. Front Matter

   Pages i-xvi

   PDF

2. Operators with Index

   1. Fredholm Operators

      B. Booss, D. D. Bleecker

      Pages 1-5

   2. Algebraic Properties. Operators of Finite Rank

      B. Booss, D. D. Bleecker

      Pages 5-12

   3. Analytic Methods. Compact Operators

      B. Booss, D. D. Bleecker

      Pages 12-25

   4. The Fredholm Alternative

      B. Booss, D. D. Bleecker

      Pages 26-34

   5. The Main Theorems

      B. Booss, D. D. Bleecker

      Pages 34-47

   6. Families of Invertible Operators. Kuipers Theorem

      B. Booss, D. D. Bleecker

      Pages 47-60

   7. Families of Fredholm Operators. Index Bundles

      B. Booss, D. D. Bleecker

      Pages 60-78

   8. Fourier Series and Integrals [Fundamental Principles]

      B. Booss, D. D. Bleecker

      Pages 79-85

   9. Wiener-Hopf Operators

      B. Booss, D. D. Bleecker

      Pages 85-102

3. Analysis on Manifolds

   1. Partial Differential Equations

      B. Booss, D. D. Bleecker

      Pages 103-125

   2. Differential Operators Over Manifolds

      B. Booss, D. D. Bleecker

      Pages 126-143

   3. Pseudo-Differential Operators

      B. Booss, D. D. Bleecker

      Pages 144-172

   4. Sobolev Spaces [Crash Course]

      B. Booss, D. D. Bleecker

      Pages 172-181

   5. Elliptic Operators over Closed Manifolds

      B. Booss, D. D. Bleecker

      Pages 182-188

   6. Elliptic Boundary-Value Systems I [Differential Operators]

      B. Booss, D. D. Bleecker

      Pages 189-198

   7. Elliptic Differential Operators of First Order with Boundary Conditions

      B. Booss, D. D. Bleecker

      Pages 199-208

   8. Elliptic Boundary-Value Systems II [Survey]

      B. Booss, D. D. Bleecker

      Pages 208-217

4. The Atiyah-Singer Index Formula

   1. Introduction to Algebraic Topology [K-Theory]

      B. Booss, D. D. Bleecker

      Pages 218-246

   2. The Index Formula in the Euclidean Case

      B. Booss, D. D. Bleecker

      Pages 246-256

Page 1 Navigate to page number of 2

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

• Book Title Topology and Analysis
• Book Subtitle The Atiyah-Singer Index Formula and Gauge-Theoretic Physics
• Authors B. Booss
  D.D. Bleecker
  
• Series Title Universitext
• DOI //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
• Softcover ISBN 978-0-387-96112-5
• eBook ISBN 978-1-4684-0627-6
• Series ISSN 0172-5939
• Series E-ISSN 2191-6675
• Edition Number 1
• Number of Pages XVI, 451
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics Real Functions
  Topology
  

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