On the cohomology rings of Hamiltonian T-spaces

الأصل · EN

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 M denote the inclusion. By a theorem of F. Kirwan K the induced map i*:Hₜ*(M) → Hₜ*(F) in equivariant cohomology is an injection. We give a simple proof of a formula of Goresky-Kottwitz-MacPherson GKM for the image of the map i*.