On the isomorphism problem for relatively hyperbolic groups.
Time and place
1 PM on Thursday, March 7th, 2013; NAC-6/113
Nicholas Touikan (Marseille)
Abstract
In 1911, Dehn posed the following question: "Is there an algorithm which can decide whether any two finite group presentations correspond to isomorphic groups?" In the late 1950s Adian and Rabin gave a negative answer to this question.
Nonetheless there have been great successes when we impose the further restriction that these group presentations belong to a given class of groups. In my talk I will survey the developments, as well as the main ideas, of the solutions to the isomorphism problem for the (very interesting) class of hyperbolic and relatively hyperbolic groups which lead up to my joint result with François Dahmani which solves the isomorphism problem for a class of groups that contains the groups that are hyperbolic relative to finitely generated nilpotent groups.
In particular, thanks to the benefit of hindsight, we are able to give a conceptually appealing "three step approach" to the solution of the isomorphism problem for relatively hyperbolic groups, which is accessible to non-specialists.
