Convexity package for momentum maps on contact manifolds
Symplectic Geometry
2014-10-01 v2 Combinatorics
Differential Geometry
Abstract
Let a torus T act effectively on a compact connected cooriented contact manifold, and let Psi be the natural momentum map on the symplectization. We prove that, if dim T > 2, the union of the origin with the image of Psi is a convex polyhedral cone, the non-zero level sets of Psi are connected (while the zero level set can be disconnected), and the momentum map is open as a map to its image. This answers a question posed by Eugene Lerman, who proved similar results when the zero level set is empty. We also analyze examples with dim T <= 2.
Keywords
Cite
@article{arxiv.0910.5637,
title = {Convexity package for momentum maps on contact manifolds},
author = {River Chiang and Yael Karshon},
journal= {arXiv preprint arXiv:0910.5637},
year = {2014}
}
Comments
39 pages. Contains small corrections and a small simplification of the argument. To appear in Algebraic and Geometric Topology.