| Description |
1 online resource (v, 84 pages) |
| Series |
Memoirs of the American Mathematical Society ; v. 261 |
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Memoirs of the American Mathematical Society.
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| Contents |
Cover -- Title page -- Introduction -- Chapter 1. Index Theory -- 1.1. Elliptic and transversally elliptic symbols -- 1.2. Functoriality -- 1.3. Clifford bundles and Dirac operators -- Chapter 2. \K-theoretic localization -- 2.1. Deformation à la Witten of Dirac operators -- 2.2. Abelian Localization formula -- 2.3. Non abelian localization formula -- Chapter 3. "Quantization commutes with Reduction" Theorems -- 3.1. The [,]=0 theorem for Clifford modules -- 3.2. The [,]=0 theorem for almost complex manifolds -- 3.3. A slice theorem for deformed symbol -- 3.4. The Hamiltonian setting |
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Chapter 4. Branching laws -- 4.1. Quasi polynomial behaviour -- 4.2. Multiplicities on a face -- Bibliography -- Back Cover |
| Summary |
The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the [Q, R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplici |
| Bibliography |
Includes bibliographical references (pages 69-71) |
| Notes |
Description based on print version record |
| Subject |
Non-Abelian groups.
|
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K-theory.
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Grupos abelianos
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Teoría K
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K-theory
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Non-Abelian groups
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| Form |
Electronic book
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| Author |
Vergne, Michèle, author.
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| ISBN |
9781470453978 |
|
1470453975 |
|
9781470453985 |
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1470453983 |
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