Convexity of Hamiltonian manifolds

Details Convexity of Hamiltonian manifolds Convexity of Hamiltonian manifolds

2001-12-13

arxiv.org/abs/math/0112144v1

J. Lie Theory 12 (2002), 571-582

Mathematics

Symplectic Geometry

12 pages, to appear in J. Lie Theory

Scientific paper

Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open onto its image. Conversely, the three properties above imply convexity. We show that most Hamiltonian manifolds occuring "in nature" are convex (e.g., if M is compact, complex algebraic, or a cotangent bundle). Moreover, every Hamiltonian manifold is locally convex. This is an expanded version of section 2 of my paper dg-ga/9712010 on Weyl groups of Hamiltonian manifolds.

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