Deciding isomorphy using Dehn fillings, the splitting case - Archive ouverte HAL
Article Dans Une Revue Inventiones Mathematicae Année : 2019

Deciding isomorphy using Dehn fillings, the splitting case

François Dahmani
Nicholas Touikan
  • Fonction : Auteur

Résumé

We solve Dehn’s isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings and the given solutions of the algorithmic problems in the parabolic groups are then used to decide if the graphs of groups have isomorphic vertex groups and, if so, whether a global isomorphism can be assembled. For the class of finitely generated nilpotent groups, we give solutions to these algorithmic problems by using the arithmetic nature of these groups and of their automorphism groups.

Dates et versions

hal-01986621 , version 1 (18-01-2019)

Identifiants

Citer

François Dahmani, Nicholas Touikan. Deciding isomorphy using Dehn fillings, the splitting case. Inventiones Mathematicae, 2019, 215 (1), pp.81-169. ⟨10.1007/s00222-018-0824-y⟩. ⟨hal-01986621⟩
28 Consultations
0 Téléchargements

Altmetric

Partager

More