The conjugacy problem for relatively hyperbolic groups

Bumagin, Inna

doi:10.2140/agt.2004.4.1013

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The conjugacy problem for relatively hyperbolic groups

Inna Bumagin

Algebraic & Geometric Topology 4 (2004) 1013–1040

DOI: 10.2140/agt.2004.4.1013

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 1125 Colonel By Drive Herzberg Building Ottawa Ontario Canada K1S 5B6

Volume 4, issue 2 (2004)