Basic Kirwan Surjectivity for K-Contact Manifolds

Abstract

We prove an analogue of Kirwan surjectivity in the setting of equivariant basic cohomology of K-contact manifolds. If the Reeb vector field induces a free $S^1$-action, the $S^1$-quotient is a symplectic manifold and our result reproduces Kirwan's surjectivity for these symplectic manifolds. We further prove a Tolman-Weitsman type description of the kernel of the basic Kirwan map for $S^1$-actions and show that torus actions on a K-contact manifold that preserve the contact form and admit 0 as a regular value of the contact moment map are equivariantly formal in the basic setting.

37 pages; proof of Lemma 4.4 corrected; unnecessary Prop. 3.17 removed; references updated and typos corrected; introductory paragraph added and minor modifications according to reviewers' suggestions

References in corpus (2)

• Torus actions whose equivariant cohomology is Cohen-Macaulay
• Topology of generalized complex quotients