Let M be a compact manifold with a Hamiltonian T action and moment map Φ. The restriction map in rational equivariant cohomology from M to a level set Φ-1(p) is a surjection, and we denote the kernel by I(p). When T has isolated fixed points, we show that I(p) distinguishes the chambers of the moment polytope for M. In particular, counting the number of distinct ideals I(p) as (p) varies over different chambers is equivalent to counting the number of chambers.
"Distinguishing the Chambers of the Moment Polytope." J. Symplectic Geom. 2 (1) 109 - 131, October, 2003.