Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 081, 17 pages      arXiv:1003.1773     http://dx.doi.org/10.3842/SIGMA.2010.081

Singular Reduction of Generalized Complex Manifolds

Timothy E. Goldberg
Donald and Helen Schort School of Mathematics and Computing Sciences, Lenoir-Rhyne University, Hickory, North Carolina 28601, USA

Received March 24, 2010, in final form October 06, 2010; Published online October 09, 2010

Abstract
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 Kähler manifolds.

Key words: generalized complex manifold; Hamiltonian action; generalized complex quotient; Lin-Tolman quotient; singular reduction.

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