Restriction map in a regular reduction of $\mathbf{SU}(n)^{2g}$

Abstract

The quasi-Hamiltonian reduction of $\mathbf{SU}(n)^{2g}$ at a regular value, in the centre of SU(n), of the moment map is isomorphic to a moduli-space of semi-stable vector bundles over a Riemann surface. We describe the restriction map from the equivariant cohomology of $\mathbf{SU}(n)^{2g}$ to the cohomology of the moduli space in terms of natural multiplicative generators of these cohomologies.