Publications mathématiques

, Volume 107, Issue 1, pp 211–290 | Cite as

The isomorphism problem for toral relatively hyperbolic groups

  • François DahmaniEmail author
  • Daniel Groves


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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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.


Conjugacy Class Parabolic Subgroup Abelian Subgroup Hyperbolic Group Isomorphism Problem 
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© 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

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