TY - JOUR

T1 - Convexity package for momentum maps on contact manifolds

AU - Chiang, River

AU - Karshon, Yael

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.2140/agt.2010.10.925

DO - 10.2140/agt.2010.10.925

M3 - Article

AN - SCOPUS:77954870907

VL - 10

SP - 925

EP - 977

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 2

ER -