25. Hausel, T., Proudfoot, N.: Abelianization for hyperkähler quotients, (to appear in Topology ), arXiv: math.SG/0310141
Abstract
We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohomology rings of a hyperpolygon space.