Buch, Englisch, 247 Seiten, Format (B × H): 156 mm x 237 mm, Gewicht: 384 g
Reihe: Modern Birkhäuser Classics
Buch, Englisch, 247 Seiten, Format (B × H): 156 mm x 237 mm, Gewicht: 384 g
Reihe: Modern Birkhäuser Classics
ISBN: 978-0-8176-8246-0
Verlag: Birkhauser Boston
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 fot 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 work revisits some fundamental concepts of the theory, and presents the application to symplectic geometry.
J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic study is certainly no exception. Reprinted as it was originally published, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics.
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Research
Autoren/Hrsg.
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Weitere Infos & Material
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.
