Distinguishing the Chambers of the Moment Polytope
Symplectic Geometry
2014-11-18 v2
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.
Cite
@article{arxiv.math/0302265,
title = {Distinguishing the Chambers of the Moment Polytope},
author = {Rebecca F. Goldin and Tara S. Holm and Lisa C. Jeffrey},
journal= {arXiv preprint arXiv:math/0302265},
year = {2014}
}
Comments
23 pages, 4 figures; To appear in Journal of Symplectic Geometry