Convexity package for momentum maps on contact manifolds

Meng-Jung Chiang, Yael Karshon

Research output: Contribution to journalArticle

Abstract

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 dim T > 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 dim T ≤ 2.

Original languageEnglish
Pages (from-to)925-977
Number of pages53
JournalAlgebraic and Geometric Topology
Volume10
Issue number2
DOIs
Publication statusPublished - 2010 Jul 29

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Momentum Map
Contact Manifold
Level Set
Convexity
Zero set
Polyhedral Cones
Convex Cone
Torus
Union

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

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Convexity package for momentum maps on contact manifolds. / Chiang, Meng-Jung; Karshon, Yael.

In: Algebraic and Geometric Topology, Vol. 10, No. 2, 29.07.2010, p. 925-977.

Research output: Contribution to journalArticle

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