Topology of generalized complex quotients

TL;DR

This paper extends classical results on equivariant cohomology to twisted generalized complex manifolds with torus actions, demonstrating Kirwan injectivity and surjectivity in this broader context.

Contribution

It proves Kirwan injectivity and surjectivity for twisted equivariant cohomology on compact twisted generalized complex manifolds with torus actions, generalizing known results.

Findings

Kirwan injectivity holds for twisted equivariant cohomology.

Kirwan surjectivity holds for twisted equivariant cohomology.

Classical cohomology results extend to twisted generalized complex settings.

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.