00000cmm a22000004a 4500 UP-99796217611212574 Buklod 20230215085534.0 m go j cr |n |||auu|a 110727s2011 xxu u eng d 9780817682477 (eBook) 0817682473 (eBook) (iLib)UPD-00215704378 DML eng DMLUC QC 20.7 M24 D85 2011eb Duistermaat, Johannes Jisse 1942- The heat kernel Lefschetz fixed point formula for the spin-c dirac operator [electronic resource] J.J. Duistermaat. New York Birkhäuser 2011. 1 online resource (xi, 247 p.). 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. IP-based subscription access limited to within on campus computer resources of the UPD University Library Website. 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 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Almost complex manifolds. Operator theory. Dirac equation. Differential topology. Mathematical physics. Electronic book. Duistermaat, J. J. 1942- (Johannes Jisse). SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007%2F978-0-8176-8247-7 FO Monograph UPD DMLR Electronic Resource