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Toric Hypersymplectic Quotients

Andrew Dancer·Andrew Swann
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Abstract

We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in R^{3n}. We give precise conditions for smoothness and non-degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations. Examples are studied, including non-trivial structures on R^{4n} and metrics on complements of hypersurfaces in compact manifolds.

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Andrew Dancer, Andrew Swann. 2004-05-06. Toric Hypersymplectic Quotients. https://arxiv.org/abs/math/0404547

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