On the Profinite Topology on Negatively Curved Groups

Abstract

Let H and K be quasiconvex subgroups of a negatively curved locally extended residually finite (LERF) group G. It is shown that if H is malnormal in G, then the double coset KH is closed in the profinite topology of G. In particular, this is true if G is the fundamental group of an atoroidal LERF hyperbolic 3-manifold, and H is the fundamental group of a totally geodesic boundary component of such manifold.