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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The conjugacy problem for relatively hyperbolic groups

Inna Bumagin

Algebraic & Geometric Topology 4 (2004) 1013–1040

arXiv: math.GR/0308171

Abstract

Solvability of the conjugacy problem for relatively hyperbolic groups was announced by Gromov [Hyperbolic groups, MSRI publications 8 (1987)]. Using the definition of Farb of a relatively hyperbolic group in the strong sense [B Farb, Relatively hyperbolic groups, Geom. Func. Anal. 8 (1998) 810–840], we prove this assertion. We conclude that the conjugacy problem is solvable for fundamental groups of complete, finite-volume, negatively curved manifolds, and for finitely generated fully residually free groups.

Keywords
negatively curved groups, algorithmic problems
Mathematical Subject Classification 2000
Primary: 20F67
Secondary: 20F10
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Publication
Received: 5 May 2002
Revised: 2 July 2003
Accepted: 4 September 2003
Published: 3 November 2004
Authors
Inna Bumagin
Department of Mathematics and Statistics, Carleton University
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Canada K1S 5B6