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

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Springer Science & Business Media, Jul 8, 2011 - Mathematics - 247 pages
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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.

 

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Contents

Chapter 2 The DolbeaultDirac Operator
7
Chapter 3 Clifford Modules
18
Chapter 4 The Spin Group and the Spinc Group
35
Chapter 5 The Spinc Dirac Operator
41
Chapter 6 Its Square
52
Chapter 7 The Heat Kernel Method
69
Chapter 8 The Heat Kernel Expansion
77
Chapter 9 The Heat Kernel on a Principal Bundle
98
Chapter 11 The HirzebruchRiemannRoch Integrand
130
Chapter 12 The Local Lefschetz Fixed Point Formula
147
Chapter 13 Characteristic Classes
157
Chapter 14 The Orbifold Version
171
Chapter 15 Application to Symplectic Geometry
187
Equivariant Forms
220
Bibliography
237
Index
245

Chapter 10 The Automorphism
117

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