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^-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.

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Published 1 January 2004