Cohomology of Generalized Complex Quotients

<div class="line" id="line-19"> Generalized complex geometry was &filig;rst introduced by N. Hitchin and then further developed by Gualtieri as a simultaneous generalization of both symplectic and complex geometries. A notion of generalized moment map and Hamiltonian action in generalized complex geometry was introduced by Tolman and the speaker a while ago. In this talk, we explain the Morse-Bott theory behind the geometry of generalized moment maps. In particular, this allows us to extend the whole Kirwan package in equivariant symplectic geometry, i.e., the Kirwan surjectivity and injectivity results, to Hamiltonian torus actions on compact generalized complex manifolds. This talk is based on a recent joint work with T. Baird.</div>