The symplectic geometry of polygons in hyperbolic 3-space

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dc.creatorKapovich, Michael
dc.creatorMillson, John J.
dc.creatorTreloar, Thomas
dc.date1999-07-22
dc.date2000-08-21
dc.date.accessioned2026-07-07T05:30:00Z
dc.date.available2026-07-07T05:30:00Z
dc.descriptionWe study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure coming from Poisson Lie theory. We construct completely integrable systems on these moduli spaces by bending n-gons along their diagonals. The results of this paper are the analogues of the results of the first two authors for n-gon linkages in Euclidean 3-space in JDG 44. We conclude by proving by a deformation argument that the moduli spaces of n-gon linkages in hyperbolic 3-space and Euclidean 3-space with the same set of side-lengths are symplectomorphic.
dc.identifierhttps://arxiv.org/abs/math/9907143
dc.identifierhttp://arxiv.org/abs/math/9907143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78860
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.titleThe symplectic geometry of polygons in hyperbolic 3-space
dc.typetext

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