The equivariant cohomology of Hamiltonian G-spaces From Residual S¹ Actions

2001/07/18 by Rebecca Goldin, Tara S. Holm
Mathematics · #math.SG #msc:53D05 #msc:53D20 #msc:55N91

paper · pdf

published as Math. Res. Let. {\bf 8} (2001), 67-78 · 13 pages, 4 figures

arxiv created 2001/07/18 · arxiv updated 2009/11/30

Abstract

We show that for a Hamiltonian action of a compact torus G on a compact, connected symplectic manifold M, the G-equivariant cohomology is determined by the residual S¹ action on the submanifolds of M fixed by codimension-1 tori. This theorem allows us to compute the equivariant cohomology of certain manifolds, which have pieces that are four-dimensional or smaller. We give several examples of the computations that this allows.

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