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arXiv · 0901.0361

Convexity properties of generalized moment maps

Yasufumi Nitta
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Abstract

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.

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Yasufumi Nitta. 2009-01-04. Convexity properties of generalized moment maps. https://arxiv.org/abs/0901.0361

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