L ²-Cohomology of Hyperkähler Quotients

Abstract:

Using an argument of Jost and Zuo, we give a criterion which implies that the L ² harmonic forms on a complete noncompact hyperkähler manifold lie in the middle dimension and are invariant under the isometry group. This is applied to various examples, and in particular gives a verification of some of the predictions of Sen on monopole moduli spaces.