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

by J.J. Duistermaat

Overview

Reprinted as it originally appeared in the 1990s,this work is as an affordable textthat will be of interest to a range of researchers in geometric analysis and mathematical physics. Thebook covers avarietyof concepts fundamental tothe 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.

Product Details

ISBN-13:	9780817682460
Publisher:	Birkhäuser Boston
Publication date:	07/08/2011
Series:	Modern Birkhäuser Classics
Edition description:	2011
Pages:	247
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

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

From the Publisher

Revisits fundamental concepts of the heat kernel Lefschetz fixed point formula for the spin-c Dirac operator, using the heat kernel theories of Berline, Getzler, and Vergne, and presents its application to symplectic geometry. Treats subjects including Clifford modules, the Hirzebruch-Riemann-Roch integrand, and the orbifold version, and offers an appendix on equivariant forms. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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