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

Let $M$ be a differentiable manifold and $G$ a compact, connected Lie group acting on M by isometries. In this paper, we study the equivariant cohomology of $\mathbf{X} = T^* M$, 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.

Keywords

equivariant cohomology, residue formulae, momentum map, symplectic quotients, stationary phase principle, resolution of singularities

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Published 8 July 2016