Localization for $K$-contact manifolds

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 $N$.

Full Text (PDF format)

Received 23 May 2017

Accepted 18 August 2018

Published 24 October 2019