Convexity properties of generalized moment maps
Abstract
Description
In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness properties for generalized moment maps. We study Hamiltonian torus actions on compact $H$-twisted generalized complex manifolds and prove that all components of the generalized moment map are Bott-Morse functions. Based on this, we shall show that the generalized moment maps have a convex image and connected fibers. Furthermore, by applying the arguments of Lerman, Meinrenken, Tolman, and Woodward \cite{Ler2} we extend our results to the case of Hamiltonian actions of general compact Lie groups on $H$-twisted generalized complex orbifolds.
25pages, to appear in J. Math. Soc. Japan. In this paper, we extend our results in arXiv:0710.3924 to the case of Hamiltonian actions of general compact Lie groups on H-twisted generalized complex orbifolds by applying the arguments of Lerman, Meinrenken, Tolman, and Woodward
25pages, to appear in J. Math. Soc. Japan. In this paper, we extend our results in arXiv:0710.3924 to the case of Hamiltonian actions of general compact Lie groups on H-twisted generalized complex orbifolds by applying the arguments of Lerman, Meinrenken, Tolman, and Woodward