Isomorphism Problem for Hyperbolic Groups and the Classification of 3-Manifolds

摘要

Using canonical representatives in hyperbolic groups and the decidability of theDiophantine theory of free semigroups with paired alphabet, the authors solve the isomorphism problem for hyperbolic groups with no small action on a real tree. The solution enables computation of the outer automorphism group of such groups and implies the homeomorphism problem for 'weakly geometric' 3-manifolds, closed hyperbolic manifolds and negatively curved ones of dimension = or > 5.