Residual finiteness, QCERF and fillings of hyperbolic groups

Agol, Ian; Groves, Daniel; Manning, Jason Fox

doi:10.2140/gt.2009.13.1043

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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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 2000

Primary: 20E26, 20F67, 20F65

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

Volume 13, issue 2 (2009)