Convexity properties of generalized moment maps

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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 [15]. 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 [13] we extend our results to the case of Hamiltonian actions of general compact Lie groups on H-twisted generalized complex orbifolds.

Original languageEnglish
Pages (from-to)1171-1204
Number of pages34
JournalJournal of the Mathematical Society of Japan
Volume61
Issue number4
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Convexity properties
  • Generalized complex structures
  • Moment maps

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