Residual finiteness, QCERF, and fillings of hyperbolic groups

Abstract

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

(v1) 22 pages, 2 figures. (v2) 24 pages, 2 figures. An error in the proof and statement of the main technical lemma was corrected, and some other small corrections and clarifications were made

References in corpus (1)

• On Quasiconvexity and Relative Hyperbolic Structures

Cited by in corpus (12)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Distinguishing geometries using finite quotients
• Separability of double cosets and conjugacy classes in 3-manifold groups
• Separation of Relatively Quasiconvex Subgroups
• Hyperbolic groups acting improperly
• Relative cubulations and groups with a 2-sphere boundary
• Quasi-hyperbolic planes in relatively hyperbolic groups
• Boundaries of Dehn fillings
• Dehn filling Dehn twists
• Hierarchies for Relatively Hyperbolic Virtually Special Groups
• Relatively geometric actions on CAT(0) cube complexes
• The quasi-isometry invariance of the Coset Intersection Complex