Mathematical Research Letters

Volume 8 (2001)

Number 1

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

Pages: 67 – 77



Rebecca Goldin (University of Maryland)

Tara S. Holm (Massachusetts Institute of Technology)


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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