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- W2951960982 abstract "This article is a result of the AIM workshop on Moment Maps and Surjectivity in Various Geometries (August 9 - 13, 2004) organized by T.Holm, E.Lerman and S.Tolman. At that workshop I was introduced to the work of T.Hausel and N.Proudfoot on hyperkahler quotients [HP]. One interesting feature of their article is that they consider integrals of equivariant forms over non-compact symplectic manifolds which do not converge, so they formally {em define} these integrals as sums over the zeroes of vector fields, as in the Berline-Vergne localization formula. In this article we introduce a geometric-analytic regularization technique which makes such integrals converge and utilizes the symplectic structure of the manifold. We also prove that the Berline-Vergne localization formula holds for these integrals as well. The key step here is to redefine the collection of integrals int_M alpha(X), X in g, as a distribution on the Lie algebra g. We expect our regularization technique to generalize to non-compact group actions extending the results of [L1,L2]." @default.
- W2951960982 created "2019-06-27" @default.
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- W2951960982 date "2004-11-29" @default.
- W2951960982 modified "2023-09-27" @default.
- W2951960982 title "Integrals of equivariant forms over non-compact symplectic manifolds" @default.
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