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

by Paul-Emile Paradan and Michele Vergne

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.

• ISBN13: 9781470435226
• Publish Date: 1 October 2020
• Publish Status: Active
• Publish Country: US
• Imprint: American Mathematical Society
• Format: Paperback
• Pages: 71
• Language: English