Witten Non Abelian Localization for Equivariant K-theory, and the [Q,R]= 0 Theorem (261) (Memoirs of the American Mathematical Society, 1257)

By Paul-Emile Paradan

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.

• Format: Paperback
• Language: English
• ISBN: 1470435225
• ISBN13: 9781470435226
• Release Date: December 2019
• Publisher: Amer Mathematical Society
• Length: 71 Pages
• Weight: 0.36 lbs.
• Dimensions: 10.0" x 0.3" x 7.0"