© 1996

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


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


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.


diffusion Dirac operator geometry Hamiltonian Laplace operator manifold operator

Authors and affiliations

  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

About the authors

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
  • Copyright Information Birkhäuser Boston 1996
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3865-8
  • Softcover ISBN 978-1-4612-5346-4
  • eBook ISBN 978-1-4612-5344-0
  • Edition Number 1
  • Number of Pages VIII, 247
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site