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

• Main Author: Duistermaat, J. J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2011.
• Series: Modern Birkhäuser Classics
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Global analysis (Mathematics).; Manifolds (Mathematics).; Operator theory.; Partial differential equations.; Differential geometry.; Mathematical physics.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.; Differential Geometry.; Analysis.; Operator Theory.; Mathematical Physics.

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...

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.