
Journal of Lie Theory 12 (2002), No. 2, 571582 Copyright Heldermann Verlag 2002 Convexity of Hamiltonian Manifolds Friedrich Knop Dept. of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A. 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. [ Fulltextpdf (208 KB)] 