The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator
(Sprache: Englisch)
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.
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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.
Klappentext zu „The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator “
From reviews of the original hard cover edition: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
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 fot 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.
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.
Inhaltsverzeichnis zu „The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator “
1 Introduction2 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
Autoren-Porträt von J.J. Duistermaat
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.
Bibliographische Angaben
- Autor: J.J. Duistermaat
- 2011, 247 Seiten, Maße: 15,6 x 23,7 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 0817682465
- ISBN-13: 9780817682460
Sprache:
Englisch
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