Algebraic and Geometric Topology 4 (2004), paper no. 43, pages 1013-1040.

The conjugacy problem for relatively hyperbolic groups

Inna Bumagin

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

AMS subject classification. Primary: 20F67. Secondary: 20F10.

DOI: 10.2140/agt.2004.4.1013

E-print: arXiv:math.GR/0308171

Submitted: 5 May 2002. (Revised: 2 July 2003.) Accepted: 4 September 2003. Published: 3 November 2004.

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Inna Bumagin
Department of Mathematics and Statistics, Carleton University
1125 Colonel By Drive, Herzberg Building
Ottawa, Ontario, Canada K1S 5B6

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