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DISTINGUISHING THE CHAMBERS OF THE MOMENT POLYTOPE

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(p) is a surjection, and we denote the kernel by Ip. When T has isolated fixed points, we show that Ip distinguishes the chambers of the moment polytope for M . In particular, counting the number of distinct ideals Ip as p varies over different chambers is equivalent to counting the number of chambers.