2016/10/31 by Lana Casselmann · 1 citation
Mathematics · #Cohomology #Differential geometry #Equivariant map #Field (mathematics) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Moment map #Symplectic geometry #Torus #math.DG #msc:53C12 #msc:53C25 #msc:53D10 #msc:53D20 #msc:55N91
paper · pdf · doi:10.1007/s10455-017-9552-6
published in Annals of Global Analysis and Geometry 52(2), 157-185 (Springer Science+Business Media) · 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
openalex created_date 2016/10/28 · openalex publication_date 2017/03/22 · arxiv created 2018/03/12 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05
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 S1-action, the S1-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 S1-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.