Hamiltonian symmetries and reduction in generalized geometry

Details Hamiltonian symmetries and reduction in generalized geometry Hamiltonian symmetries and reduction in generalized geometry

2005-09-05

arxiv.org/abs/math/0509060v3

Mathematics

Differential Geometry

LaTeX 18 pages. Added references, corrected typos and improved exposition

Scientific paper

A closed 3-form $H \in \Omega^3_0(M)$ defines an extension of $\Gamma(TM)$ by $\Omega^2_0(M)$. This fact leads to the definition of the group of $H$-twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold. The Hamiltonian reduction in the category of generalized complex geometry is then constructed. The definitions and constructions are natural extensions of the corresponding ones in the symplectic geometry. We describe cutting in generalized complex geometry to show that it's a general phenomenon in generalized geometry that topology change is often accompanied by twisting (class) change.

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