Separation of Relatively Quasiconvex Subgroups

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in r...

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Bibliographic Details
Published in:arXiv.org 2010-05
Main Authors: Jason Fox Manning, Martinez-Pedroza, Eduardo
Format: Article
Language:English
Subjects:
Lattices
Manifolds
Subgroups
Online Access:Get full text
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Summary:Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that LERF for finite volume hyperbolic 3-manifolds would follow from LERF for closed hyperbolic 3-manifolds. The method is to reduce, via combination and filling theorems, the separability of a quasiconvex subgroup of a relatively hyperbolic group G to the separability of a quasiconvex subgroup of a hyperbolic quotient G/N. A result of Agol, Groves, and Manning is then applied.
ISSN:2331-8422
DOI:10.48550/arxiv.0811.4001