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

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

Part of the Memoirs of the American Mathematical Society series

Paperback / softback

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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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