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Toric hypersymplectic quotients
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Journal Article
Toric hypersymplectic quotients
2007
Overview
We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R4d\\mathbb {R}^{4d} by the action of a compact Abelian group. These 4n4n-dimensional quotients carry a multi-Hamilitonian action of an nn-torus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in R3n\\mathbb {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 R4n\\mathbb {R}^{4n} and metrics on complements of hypersurfaces in compact manifolds.
Publisher
American Mathematical Society
