Distinguishing the Chambers of the Moment Polytope

Details Distinguishing the Chambers of the Moment Polytope Distinguishing the Chambers of the Moment Polytope

2003-02-21

arxiv.org/abs/math/0302265v2

Journal of Symplectic Geometry, vol. 2, no. 1 (2003), pp. 109-131.

Mathematics

Symplectic Geometry

23 pages, 4 figures; To appear in Journal of Symplectic Geometry

Scientific paper

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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