Separation of Relatively Quasiconvex Subgroups

Details Separation of Relatively Quasiconvex Subgroups Separation of Relatively Quasiconvex Subgroups

2008-11-25

arxiv.org/abs/0811.4001v3

Mathematics

Group Theory

22 pages, 2 figures. New version has numbering matching with the published version in the Pacific Journal of Mathematics, 244

Scientific paper

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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