D. Holt, The word and conjugacy problems in hyperbolic groups

We review the definition and fundamental properties of (word) hyperbolic groups. In particular, a finitely generated group is hyperbolic if and only if it has a Dehn algorithm. This implies that the word problem can be solved in linear time. A stronger result is that any word in the generators of a hyperbolic group can be reduced to a normal form (the so-called shortlex normal form) in linear time. We shall report on a recent result of Holt and Epstein that the conjugacy problem in a hyperbolic group is solvable in linear time. Finally, we discuss the relationships between our methods and recent work Bridson and Howie on the conjugacy of finite subsets in hyperbolic groups.
A.J. Duncan
Last modified: Wed Jun 2 17:51:05 BST 2004