The isomorphism problem for toral relatively hyperbolic groups

François Dahmani; Daniel Groves

Publications Mathématiques de l'IHÉS (2008)

  • Volume: 107, page 211-290
  • ISSN: 0073-8301

Abstract

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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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

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Dahmani, François, and Groves, Daniel. "The isomorphism problem for toral relatively hyperbolic groups." Publications Mathématiques de l'IHÉS 107 (2008): 211-290. <http://eudml.org/doc/273597>.

@article{Dahmani2008,
abstract = {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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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 $n\ge 3$. 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.},
author = {Dahmani, François, Groves, Daniel},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {isomorphism problem; relatively hyperbolic groups; hyperbolic manifolds; finitely presented groups; parabolic subgroups; torsionfree hyperbolic groups; limit groups; algorithms; JSJ decompositions},
language = {eng},
pages = {211-290},
publisher = {Institut des hautes études scientifiques},
title = {The isomorphism problem for toral relatively hyperbolic groups},
url = {http://eudml.org/doc/273597},
volume = {107},
year = {2008},
}

TY - JOUR
AU - Dahmani, François
AU - Groves, Daniel
TI - The isomorphism problem for toral relatively hyperbolic groups
JO - Publications Mathématiques de l'IHÉS
PY - 2008
PB - Institut des hautes études scientifiques
VL - 107
SP - 211
EP - 290
AB - 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 $n\ge 3$. 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.
LA - eng
KW - isomorphism problem; relatively hyperbolic groups; hyperbolic manifolds; finitely presented groups; parabolic subgroups; torsionfree hyperbolic groups; limit groups; algorithms; JSJ decompositions
UR - http://eudml.org/doc/273597
ER -

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