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

Author:   Paul-Emile Paradan ,  Michele Vergne
Publisher:   American Mathematical Society
ISBN:  

9781470435226


Pages:   71
Publication Date:   30 December 2019
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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Witten Non Abelian Localization for Equivariant K-theory, and the $[Q,R]=0$ Theorem


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Overview

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.

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Author:   Paul-Emile Paradan ,  Michele Vergne
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.180kg
ISBN:  

9781470435226


ISBN 10:   1470435225
Pages:   71
Publication Date:   30 December 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Introduction Index theory $\mathbf{K}$-theoretic localization ``Quantization commutes with reduction'' theorems Branching laws Bibliography.

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Paul-Emile Paradan, Universite de Montpellier, France. Michele Vergne, Universite de Paris 7, France.

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