Topology of generalized complex quotients

Abstract

Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold $M$. We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these two results hold for the twisted equivariant cohomology as well.

33 pages, substantial changes made, expositions on twisted equivariant cohomology improved

References in corpus (5)

• Generalized geometry and the Hodge decomposition
• Hamiltonian symmetries and reduction in generalized geometry
• Generalized geometry, equivariant $\bar{\partial }\partial$-lemma, and torus actions
• Convexity properties for generalized moment maps I
• The Equivariant cohomology theory of twisted generalized complex manifolds

Cited by in corpus (6)

• LA-Courant algebroids and their applications
• The GIT aspect of generalized K$\ddot{a}$hler reduction. I
• Singular Reduction of Generalized Complex Manifolds
• Basic Kirwan Surjectivity for K-Contact Manifolds
• Chern-Weil homomorphism in twisted equivariant cohomology
• Generalized complex hamiltonian torus actions: Examples and constraints