Toric Hypersymplectic Quotients

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dc.creatorDancer, Andrew
dc.creatorSwann, Andrew
dc.date2004-04-30
dc.date2004-05-06
dc.date.accessioned2026-07-07T05:07:49Z
dc.date.available2026-07-07T05:07:49Z
dc.descriptionWe 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.
dc.description26 pages, 6 figures, small linguistic corrections
dc.identifierhttps://arxiv.org/abs/math/0404547
dc.identifierhttp://arxiv.org/abs/math/0404547
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71016
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject53C25; 53D20, 53C55, 57S15
dc.titleToric Hypersymplectic Quotients
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