On the cohomology rings of Hamiltonian T-spaces

Details On the cohomology rings of Hamiltonian T-spaces On the cohomology rings of Hamiltonian T-spaces

1998-12-01

arxiv.org/abs/math/9812006v2

Mathematics

Differential Geometry

correction to references

Scientific paper

Let $M$ be a symplectic manifold equipped with a Hamiltonian action of a torus $T$. Let $F$ denote the fixed point set of the $T$-action and let $i:F\hookrightarrow M$ denote the inclusion. By a theorem of F. Kirwan \cite{K} the induced map $i^*:H_T^*(M) \to H_T^*(F)$ in equivariant cohomology is an injection. We give a simple proof of a formula of Goresky-Kottwitz-MacPherson \cite{GKM} for the image of the map $i^*$.

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