The equivariant cohomology of Hamiltonian $G$-spaces From Residual $S^1$ Actions

Details The equivariant cohomology of Hamiltonian $G$-spaces From Residual $S^1$ Actions The equivariant cohomology of Hamiltonian $G$-spaces From Residual $S^1$ Actions

2001-07-18

arxiv.org/abs/math/0107131v1

Math. Res. Let. {\bf 8} (2001), 67-78

Mathematics

Symplectic Geometry

13 pages, 4 figures

Scientific paper

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 $S^1$ 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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