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

Reprinted as it originally appeared in the 1990s,?this work is as an affordable text?that will be of interest to a range of researchers in geometric analysis and mathematical physics. The?book covers a?variety?of concepts fundamental to?the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet, and Vergne. True to the precision and clarity for which J.J. Duistermaat was so well known, the exposition is elegant and concise.

Written by one of the leading geometric analysts of the late 20th century, this soft cover reprint covers concepts fundamental to the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet and Vergne.?
1 Introduction.- 2 The Dolbeault-Dirac Operator.- 3 Clifford Modules.- 4 The Spin Group and the Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 Its Square.- 7 The Heat Kernel Method.- 8 The Heat Kernel Expansion.- 9 The Heat Kernel on a Principal Bundle.- 10 The Automorphism.- 11 The Hirzebruch-Riemann-Roch Integrand.- 12 The Local Lefschetz Fixed Point Formula.- 13 Characteristic Case.- 14 The Orbifold Version.- 15 Application to Symplectic Geometry.- 16 Appendix: Equivariant Forms.

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

Interest in the spin-c Dirac operator originally came about from the study of complexl;