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E-raamat: Witten Non Abelian Localization for Equivariant K-theory, and the $[ Q,R]=0$ Theorem

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Paradan and Vergne have two goals here. The first is to obtain a non-abelian localization theorem when M is any even dimensional compact manifold: following an idea of E. Witten, they deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Their second goal is to use this general approach the reprove the [ Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case, and they obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of general spinc Dirac operators. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)
Introduction 1(6)
Chapter 1 Index Theory
7(14)
1.1 Elliptic and transversally elliptic symbols
7(3)
1.2 Functoriality
10(3)
1.3 Chfford bundles and Dirac operators
13(8)
Chapter 2 K-theoretic localization
21(16)
2.1 Deformation a la Witten of Dirac operators
21(6)
2.2 Abelian Localization formula
27(3)
2.3 Non abelian localization formula
30(7)
Chapter 3 "Quantization commutes with Reduction" Theorems
37(26)
3.1 The [ Q,R] =0 theorem for Clifford modules
37(3)
3.2 The [ Q, R] = 0 theorem for almost complex manifolds
40(5)
3.3 A slice theorem for deformed symbol
45(3)
3.4 The Hamiltonian setting
48(15)
Chapter 4 Branching laws
63(6)
4.1 Quasi polynomial behaviour
64(2)
4.2 Multiplicities on a face
66(3)
Bibliography 69
Paul-Emile Paradan, Universite de Montpellier, France.

Michele Vergne, Universite de Paris 7, France.