Journal of Lie Theory
Vol. 12, No. 2, pp. 571--582 (2002)
Convexity of Hamiltonian manifolds
Friedrich KnopF. Knop
Department of Mathematics
New Brunswick NJ 08903
Abstract: We study point set topological properties of the moment map. In particular, we introduce the notion of a convex Hamiltonian manifold. This notion combines convexity of the momentum image and connectedness of moment map fibers with a certain openness requirement for the moment map. We show that convexity rules out many pathologies for moment maps. Then we show that the most important classes of Hamiltonian manifolds (e.g., unitary vector spaces, compact manifolds, or cotangent bundles) are in fact convex. Moreover, we prove that every Hamiltonian manifold is locally convex.
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Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.