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arXiv · 0910.5637

Convexity package for momentum maps on contact manifolds

River Chiang·Yael Karshon
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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.

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BibTeXRIS

River Chiang, Yael Karshon. 2010-03-10. Convexity package for momentum maps on contact manifolds. https://doi.org/10.2140/agt.2010.10.925

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