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Abelianization for hyperkahler quotients

Tamas Hausel·Nicholas Proudfoot
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Abstract

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.

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Tamas Hausel, Nicholas Proudfoot. 2003-10-09. Abelianization for hyperkahler quotients. https://arxiv.org/abs/math/0310141

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