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

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 ma...

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Bibliographic Details
Main Author: Duistermaat, J.J.
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 2011, 2011
Edition:1st ed. 2011
Series:Modern Birkhäuser Classics
Subjects:
Geometry, Differential
Mathematical Analysis
Analysis
Mathematical Physics
Operator Theory
Manifolds (mathematics)
Differential Geometry
Differential Equations
Global Analysis (mathematics)
Global Analysis And Analysis On Manifolds
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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

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