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

  • J. J. Duistermaat

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. J. J. Duistermaat
    Pages 1-5
  3. J. J. Duistermaat
    Pages 7-17
  4. J. J. Duistermaat
    Pages 19-33
  5. J. J. Duistermaat
    Pages 35-40
  6. J. J. Duistermaat
    Pages 41-51
  7. J. J. Duistermaat
    Pages 53-68
  8. J. J. Duistermaat
    Pages 69-75
  9. J. J. Duistermaat
    Pages 77-97
  10. J. J. Duistermaat
    Pages 99-115
  11. J. J. Duistermaat
    Pages 117-129
  12. J. J. Duistermaat
    Pages 131-145
  13. J. J. Duistermaat
    Pages 147-156
  14. J. J. Duistermaat
    Pages 157-170
  15. J. J. Duistermaat
    Pages 171-186
  16. J. J. Duistermaat
    Pages 187-219
  17. J. J. Duistermaat
    Pages 221-235
  18. Back Matter
    Pages 237-247

About this book

Introduction

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.

Keywords

diffusion Dirac operator geometry Hamiltonian Laplace operator manifold operator

Authors and affiliations

  • J. J. Duistermaat
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

Bibliographic information