Полное описание

Duistermaat, J. J. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator / by J. J. Duistermaat. - Electronic text data. - Boston : Birkhäuser, 2011. - (Modern Birkhäuser Classics). - URL: http://dx.doi.org/10.1007/978-0-8176-8247-7. - Загл. с экрана. - ISBN 978-0-8176-8247-7. - DOI 10.1007/978-0-8176-8247-7. - Текст : электронный.
Содержание:
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.

ГРНТИ	УДК
27.39.19	517.43
29.05.15	530.145

Рубрики:
mathematics
mathematical analysis
analysis (Mathematics)
global analysis (Mathematics)
manifolds (Mathematics)
operator theory
partial differential equations
differential geometry
mathematical physics
mathematics
global Analysis and Analysis on Manifolds
partial Differential Equations
differential Geometry
analysis
operator Theory
mathematical Physics

Аннотация: 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.

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