The Isomorphism Problem for All Hyperbolic Groups

International audienceWe give a solution to Dehn’s isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to Whitehead’s problem asking whether two tuples of elements of a hyperbolic group G are in the same orbit under the action of Aut(G). We also get an algorithm computing a generating set of the group of automorphisms of a hyperbolic group preserving a peripheral structure