Witten non abelian localization for equivariant K-theory, and the [Q, R] 0 theorem
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Bibliographic Information
Witten non abelian localization for equivariant K-theory, and the [Q, R] = 0 theorem
（Memoirs of the American Mathematical Society, no. 1257）
American Mathematical Society, c2019
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"September 2019, volume 261, number 1257 (first of 7 numbers)"
Includes bibliographical reference (p. 69-71)
Description and Table of Contents
Description
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 multiplicities of the index of general $spin^c$ Dirac operators.
Table of Contents
Introduction
Index theory
$\mathbf{K}$-theoretic localization
``Quantization commutes with reduction'' theorems
Branching laws
Bibliography.
by "Nielsen BookData"