Open Access
Translator Disclaimer
2010 Convexity package for momentum maps on contact manifolds
River Chiang, Yael Karshon
Algebr. Geom. Topol. 10(2): 925-977 (2010). DOI: 10.2140/agt.2010.10.925


Let a torus T act effectively on a compact connected cooriented contact manifold, and let Ψ 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 Ψ is a convex polyhedral cone, the nonzero level sets of Ψ 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 dimT2.


Download Citation

River Chiang. Yael Karshon. "Convexity package for momentum maps on contact manifolds." Algebr. Geom. Topol. 10 (2) 925 - 977, 2010.


Received: 5 November 2009; Revised: 25 February 2010; Accepted: 2 March 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1206.53082
MathSciNet: MR2629771
Digital Object Identifier: 10.2140/agt.2010.10.925

Primary: 53D10 , 53D20
Secondary: 52B99

Keywords: contact manifold , convexity , momentum map , torus action

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.10 • No. 2 • 2010
Back to Top