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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

  • Book
  • © 1996

Overview

Authors:
  1. J. J. Duistermaat

    1. Mathematisch Instituut, Universiteit Utrecht, Utrecht, The Netherlands

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 18)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • J. J. Duistermaat
    Pages 1-5

  3. The Dolbeault-Dirac Operator

    • J. J. Duistermaat
    Pages 7-17

  4. Clifford Modules

    • J. J. Duistermaat
    Pages 19-33

  5. The Spin Group and the Spin-c Group

    • J. J. Duistermaat
    Pages 35-40

  6. The Spin-c Dirac Operator

    • J. J. Duistermaat
    Pages 41-51

  7. Its Square

    • J. J. Duistermaat
    Pages 53-68

  8. The Heat Kernel Method

    • J. J. Duistermaat
    Pages 69-75

  9. The Heat Kernel Expansion

    • J. J. Duistermaat
    Pages 77-97

  10. The Heat Kernel on a Principal Bundle

    • J. J. Duistermaat
    Pages 99-115

  11. The Automorphism

    • J. J. Duistermaat
    Pages 117-129

  12. The Hirzebruch-Riemann-Roch Integrand

    • J. J. Duistermaat
    Pages 131-145

  13. The Local Lefschetz Fixed Point Formula

    • J. J. Duistermaat
    Pages 147-156

  14. Characteristic Classes

    • J. J. Duistermaat
    Pages 157-170

  15. The Orbifold Version

    • J. J. Duistermaat
    Pages 171-186

  16. Application to Symplectic Geometry

    • J. J. Duistermaat
    Pages 187-219

  17. Appendix: Equivariant Forms

    • J. J. Duistermaat
    Pages 221-235

  18. Back Matter

    Pages 237-247
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Keywords

About this book

When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug­ gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.

Authors and Affiliations

  • Mathematisch Instituut, Universiteit Utrecht, Utrecht, The Netherlands

    J. J. Duistermaat

About the author

Hans Duistermaat was a geometric analyst, who unexpectedly passed away in March 2010. His research encompassed many different areas in mathematics: ordinary differential equations, classical mechanics, discrete integrable systems, Fourier integral operators and their application to partial differential equations and spectral problems, singularities of mappings, harmonic analysis on semisimple Lie groups, symplectic differential geometry, and algebraic geometry. He was (co-)author of eleven books.

Duistermaat was affiliated to the Mathematical Institute of Utrecht University since 1974 as a Professor of Pure and Applied Mathematics. During the last five years he was honored with a special professorship at Utrecht University endowed by the Royal Netherlands Academy of Arts and Sciences. He was also a member of the Academy since 1982. He had 23 PhD students.

Bibliographic Information

  • Book Title: The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

  • Authors: J. J. Duistermaat

  • Series Title: Progress in Nonlinear Differential Equations and Their Applications

  • DOI: https://doi.org/10.1007/978-1-4612-5344-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1996

  • Softcover ISBN: 978-1-4612-5346-4Published: 21 October 2011

  • eBook ISBN: 978-1-4612-5344-0Published: 01 December 2013

  • Series ISSN: 1421-1750

  • Series E-ISSN: 2374-0280

  • Edition Number: 1

  • Number of Pages: VIII, 247

  • Topics: Analysis

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