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Toric hypersymplectic quotients

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We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space ℝ4d by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an ntorus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in ℝ3n. 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 and metrics on complements of hypersurfaces in compact manifolds.

OriginalsprogEngelsk
TidsskriftTransactions of the American Mathematical Society
Vol/bind359
Nummer3
Sider (fra-til)1265-1284
Antal sider20
ISSN0002-9947
DOI
StatusUdgivet - 1 mar. 2007
Eksternt udgivetJa

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