Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomology

Abstract

Let $M$ be a smooth manifold and $G$ a compact connected Lie group acting on $M$ by isometries. In this paper, we study the equivariant cohomology of $\mathbf{X}=T^{\ast }M$, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain residue formulae. In case that $\mathbf{X}$ is a compact symplectic manifold with a Hamiltonian $G$-action, similar residue formulae were derived by Jeffrey, Kirwan et al.

arXiv comment53 pages. arXiv admin note: substantial text overlap with arXiv:1001.1515