The conjugacy problem for relatively hyperbolic groups

Abstract

Solvability of the conjugacy problem for relatively hyperbolic groups was announced by Gromov Using the definition of Farb of a relatively hyperbolic group in the strong sense [14], 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.