Publications mathématiques

, Volume 107, Issue 1, pp 211–290

The isomorphism problem for toral relatively hyperbolic groups


DOI: 10.1007/s10240-008-0014-3

Cite this article as:
Dahmani, F. & Groves, D. Publ.math.IHES (2008) 107: 211. doi:10.1007/s10240-008-0014-3


We provide a solution to the isomorphism problem for torsion-free relatively hyperbolic groups with abelian parabolics. As special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]). We also give a solution to the homeomorphism problem for finite volume hyperbolic n-manifolds, for n≥3. In the course of the proof of the main result, we prove that a particular JSJ decomposition of a freely indecomposable torsion-free relatively hyperbolic group with abelian parabolics is algorithmically constructible.

Copyright information

© IHES and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulouseUniversité Paul Sabatier, Toulouse IIIToulouse, cedex 9France
  2. 2.MSCS UIC 322 SEO, M/C 249ChicagoUSA