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

  • Authors
  • J. J. Duistermaat
Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xi
  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

Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Kähler case the Dolbeault operator is no longer suitable for getting local formulas for the Riemann–Roch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heat kernels theory of Berline, Getzler, and Vergne, this work revisits some fundamental concepts of the theory, and presents the application to symplectic geometry.

J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic study is certainly no exception. Reprinted as it was originally published, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics.

Overall this is a carefully written, highly readable book on a very beautiful subject. —Mathematical Reviews

The book of J.J. Duistermaat is a nice introduction to analysis related [to the] spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. —EMS Newsletter

The author's book is a marvelous introduction to [these] objects and theories. —Zentralblatt MATH

Keywords

Dirac operator Laplace operator Lefschetz fixed point formula differential topology heat kernels spin-c group symplectic geometry

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8247-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8246-0
  • Online ISBN 978-0-8176-8247-7