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Article Dans Une Revue Memoirs of the American Mathematical Society Année : 2018

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

Résumé

The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the Hamiltonian case, and we 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 (see preprint arXiv:1411.7772).
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Dates et versions

hal-01145354 , version 1 (24-04-2015)
hal-01145354 , version 2 (08-01-2016)

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Paul-Emile Paradan, Michèle Vergne. Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem. Memoirs of the American Mathematical Society, inPress, ⟨10.1090/memo/1257⟩. ⟨hal-01145354v2⟩
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