Convexity package for momentum maps on contact manifolds

Details Convexity package for momentum maps on contact manifolds Convexity package for momentum maps on contact manifolds

2009-10-29

arxiv.org/abs/0910.5637v2

Algebraic & Geometric Topology 10 (2010) 925-977

Mathematics

Symplectic Geometry

39 pages. Contains small corrections and a small simplification of the argument. To appear in Algebraic and Geometric Topology

Scientific paper

10.2140/agt.2010.10.925

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.

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