#### Volume 10, issue 2 (2010)

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Convexity package for momentum maps on contact manifolds

### River Chiang and Yael Karshon

Algebraic & Geometric Topology 10 (2010) 925–977
##### 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 $dimT$ is bigger than 2, the union of the origin with the image of $\Psi$ is a convex polyhedral cone, the nonzero 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 $dimT\le 2$.

##### Keywords
momentum map, contact manifold, torus action, convexity
##### Mathematical Subject Classification 2000
Primary: 53D10, 53D20
Secondary: 52B99
##### Publication
Revised: 25 February 2010
Accepted: 2 March 2010
Published: 17 April 2010
##### Authors
 River Chiang Department of Mathematics National Cheng Kung University Tainan 701 Taiwan Yael Karshon Department of Mathematics University of Toronto Toronto, Ontario M5S 2E4 Canada http://www.math.toronto.edu/karshon/