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 m...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Duistermaat, J.J (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2011.
Edition:1st ed. 2011.
Series:Modern Birkhäuser Classics,
Subjects:
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential equations.
Geometry, Differential.
Mathematical analysis.
Operator theory.
Mathematical physics.
Global Analysis and Analysis on Manifolds.
Differential Equations.
Differential Geometry.
Analysis.
Operator Theory.
Mathematical Physics.
Online Access:Texto Completo
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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