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Distinguishing the Chambers of the Moment Polytope

Rebecca F. Goldin·Tara S. Holm·Lisa C. Jeffrey
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Abstract

Let M be a compact manifold with a Hamiltonian T action and moment map Phi. The restriction map in equivariant cohomology from M to a level set Phi^{-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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Rebecca F. Goldin, Tara S. Holm, Lisa C. Jeffrey. 2003-09-30. Distinguishing the Chambers of the Moment Polytope. https://arxiv.org/abs/math/0302265

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