  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 $i^*$.
