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.Comment: (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 mad