Hamiltonian symmetries and reduction in generalized geometry

Abstract

A closed 3-form $H\in {\Omega }_0^3(M)$ defines an extension of $\Gamma (TM)$ by ${\Omega }_0^2(M)$. 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.

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

References in corpus (13)

• Reduction of Courant algebroids and generalized complex structures
• Instantons, Poisson structures and generalized Kaehler geometry
• Symmetries in generalized Kähler geometry
• Chern character in twisted K-theory: equivariant and holomorphic cases
• Kaehler reduction of metrics with holonomy G_2
• Singular reduction of implicit Hamiltonian systems
• Reduction of Generalized Complex Structures
• Reduction of Vaisman structures in complex and quaternionic geometry
• Hyperkahler analogues of Kahler quotients
• Locally conformal Kaehler reduction
• Severi varieties and holomorphic nilpotent orbits
• Kaehler spaces, nilpotent orbits, and singular reduction
• Cayley 4-frames and a quaternion-Kähler reduction related to Spin(7)

Cited by in corpus (21)

• Reduction of Courant algebroids and generalized complex structures
• Symmetries in generalized Kähler geometry
• Reduction of Generalized Complex Structures
• T-duality and Generalized Kahler Geometry
• LA-Courant algebroids and their applications
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• Reduction of twisted generalized Kähler structure
• Generalized geometry, equivariant $\bar{\partial }\partial$-lemma, and torus actions
• Topology of generalized complex quotients
• The Large Vector Multiplet Action
• Reduction and submanifolds of generalized complex manifolds
• Moser Lemma in Generalized Complex Geometry
• Group actions on dg-manifolds and Exact Courant algebroids
• Complex Dirac structures: invariants and local structure
• Dissections and automorphisms of regular Courant algebroids
• Singular Reduction of Generalized Complex Manifolds
• Generalized K$\ddot{a}$hler Geometry in Kazama-Suzuki coset models
• Extended manifolds and extended equivariant cohomology
• Generalized Complex Submanifolds
• Chern-Weil homomorphism in twisted equivariant cohomology
• Generalized complex hamiltonian torus actions: Examples and constraints