Singular Reduction of Generalized Complex Manifolds

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Li...

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Bibliographic Details
Published inarXiv.org
Main Author Goldberg, Timothy E
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.10.2010
Subjects
Lie groups
Manifolds
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Mathematics - Symplectic Geometry
Partitions
Physics - Mathematical Physics
Reduction
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Summary:In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for reduction of Hamiltonian generalized K\"ahler manifolds.
ISSN:2331-8422
DOI:10.48550/arxiv.1003.1773