Toric Hypersymplectic Quotients
微分几何
2007-05-23 v2 辛几何
摘要
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.
引用
@article{arxiv.math/0404547,
title = {Toric Hypersymplectic Quotients},
author = {Andrew Dancer and Andrew Swann},
journal= {arXiv preprint arXiv:math/0404547},
year = {2007}
}
备注
26 pages, 6 figures, small linguistic corrections