| Description |
1 online resource (ix, 247 pages) |
| Series |
Modern Birkhäuser classics |
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Modern Birkhäuser classics.
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| 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 |
| Summary |
Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Kähler casethe 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. J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic studyis certainly no exception. Reprinted as it was originally published, this workis as an affordable textthat will be of interest to a range of researchers in geometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject.-Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[to the]spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic.-EMS Newsletter The author's book is a marvelous introduction to [these] objects and theories.-Zentralblatt MATH |
| Notes |
"Reprint of the 1996 edition." |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Almost complex manifolds.
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Operator theory.
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Dirac equation.
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Differential topology.
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Mathematical physics.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Almost complex manifolds
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Differential topology
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Dirac equation
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Mathematical physics
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Operator theory
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| Form |
Electronic book
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| ISBN |
9780817682477 |
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0817682473 |
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0817682465 |
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9780817682460 |
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