2017/03/01 by Lana Casselmann, Jonathan Fisher, Casselmann, L. +1
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1703.00333
openalex publication_date 2017/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an analogue of the Atiyah-Bott-Berline-Vergne localization formula in the setting of equivariant basic cohomology of K-contact manifolds. As a consequence, we deduce analogues of Witten's nonabelian localization and the Jeffrey-Kirwan residue formula, which relate equivariant basic integrals on a contact manifold M to basic integrals on the contact quotient M0 := μ-1(0)/G, where μ denotes the contact moment map for the action of a torus G. In the special case that M → N is an equivariant Boothby-Wang fibration, our formulae reduce to the usual ones for the symplectic manifold N.