Convexity properties of generalized moment maps
Abstract
In this paper, we consider generalized moment maps for Hamiltonian actions on -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 -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 -twisted generalized complex orbifolds.
Keywords
Cite
@article{arxiv.0901.0361,
title = {Convexity properties of generalized moment maps},
author = {Yasufumi Nitta},
journal= {arXiv preprint arXiv:0901.0361},
year = {2009}
}
Comments
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