Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator - 18

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.