Witten non abelian localization for equivariant K-theory, and the [Q, R]=0 theorem /

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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Paradan, Paul-Emile (Author), Vergne, Michèle (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence : American Mathematical Society, [2019].
Series:Memoirs of the American Mathematical Society.
Subjects:
Non-Abelian groups.
K-theory.
Groupes non abéliens.
K-théorie.
Grupos abelianos
Teoría K
K-theory
Non-Abelian groups
Online Access:Texto completo
Table of 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
  • Chapter 4. Branching laws
  • 4.1. Quasi polynomial behaviour
  • 4.2. Multiplicities on a face
  • Bibliography
  • Back Cover

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