Constructing geometrically infinite groups on boundaries of deformation spaces

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dc.creatorOhshika, Ken'ichi
dc.date2008-09-08
dc.date.accessioned2026-07-07T10:01:21Z
dc.date.available2026-07-07T10:01:21Z
dc.descriptionConsider a geometrically finite Kleinian group $G$ without parabolic or elliptic elements, with its Kleinian manifold $M=(\H^3\cup Ω_G)/G$. Suppose that for each boundary component of $M$, either a maximal and connected measured lamination in the Masur domain or a marked conformal structure is given. In this setting, we shall prove that there is an algebraic limit $Γ$ of quasi-conformal deformations of $G$ such that there is a homeomorphism $h$ from $\mathrm{Int} M$ to $\H^3/Γ$ compatible with the natural isomorphism from $G$ to $Γ$, the given laminations are unrealisable in $\H^3/Γ$, and the given conformal structures are pushed forward by $h$ to those of $\H^3/Γ$. Based on this theorem and its proof, in the subsequent paper, the Bers-Thurston conjecture, saying that every finitely generated Kleinian group is an algebraic limit of quasi-conformal deformations of minimally parabolic geometrically finite group, is proved using recent solutions of Marden's conjecture by Agol, Calegari-Gabai, and the ending lamination conjecture by Minsky collaborating with Brock, Canary and Masur.
dc.descriptionThis is a revised version of my preprint which I disseminated some years ago
dc.identifierhttps://arxiv.org/abs/0809.1261
dc.identifierhttp://arxiv.org/abs/0809.1261
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168605
dc.subjectGeometric Topology
dc.subject57M50; 30F40
dc.titleConstructing geometrically infinite groups on boundaries of deformation spaces
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