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Residual finiteness, QCERF and fillings of hyperbolic groups

Ian Agol, Daniel Groves and Jason Fox Manning

Geometry & Topology 13 (2009) 1043–1073

DOI: 10.2140/gt.2009.13.1043
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.

Keywords

hyperbolic group, quasiconvex subgroup, residually finite, LERF
Mathematical Subject Classification

Primary: 20E26, 20F65, 20F67
References
Publication

Received: 10 March 2008
Accepted: 4 January 2009
Published: 21 January 2009
Proposed: Benson Farb
Seconded: Mike Freedman, Walter Neumann
Authors
Ian Agol
University of California, Berkeley
970 Evans Hall #3840
Berkeley, CA 94720-3840
USA
Daniel Groves
Department of Math, Stats and Comp Sci
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607-7045
USA
Jason Fox Manning
Department of Mathematics
SUNY at Buffalo
Buffalo, NY 14260-2900
USA