Localization for $K$-Contact Manifolds

Abstract

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 $M_0:={\mu }^{-1}(0)/G$, where $\mu$ denotes the contact moment map for the action of a torus $G$. In the special case that $M\to N$ is an equivariant Boothby-Wang fibration, our formulae reduce to the usual ones for the symplectic manifold $N$.

33 pages; proof of Lemma 3.5 corrected; minor corrections; to appear in J. Sympl. Geom