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arXiv · 0811.4001

Separation of Relatively Quasiconvex Subgroups

Jason Fox Manning·Eduardo Martinez-Pedroza
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Abstract

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.

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Jason Fox Manning, Eduardo Martinez-Pedroza. 2010-05-12. Separation of Relatively Quasiconvex Subgroups. https://doi.org/10.2140/pjm.2010.244.309

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