Equivariant Integration formulæ in HyperKähler Geometry

Details Equivariant Integration formulæ in HyperKähler Geometry Equivariant Integration formulæ in HyperKähler Geometry

2004-02-18

arxiv.org/abs/math/0402297v2

Mathematics

Differential Geometry

27 pages, LaTeX. Chapter 2 of the Author's Ph.D Thesis. Minor Corrections and an extra remark (3.2) on how hyperK\"ahler integ

Scientific paper

Lisa Jeffrey and Frances Kirwan developed an integration theory for symplectic reductions. That is, given a symplectic manifold with symplectic group action, they developed a way of pulling the integration of forms on the reduction back to an integration of group-equivariant forms on the original space. We seek an analogue of the symplectic integration formula as developed by for the hyperKahler case. This is almost straightforward, but we have to overcome such obstacles as the lack of a hyper-Darboux theorem and the lack of compactness in the case of hyperKahler reduction.

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