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

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概要 Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Kähler casethe Dolbeault operator is no longer suitable for getting local for...mulas 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 workrevisits 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 studyis certainly no exception. Reprinted as it was originally published,this workis as an affordable textthat 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続きを見る
目次 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.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2011 English/International

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登録日 2020.06.27
更新日 2020.06.28