  We study an integration theory in circle equivariant cohomology in order to
prove a theorem relating the cohomology ring of a hyperkahler 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.
