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The isomorphism problem for toral relatively hyperbolic groups

François DahmaniDaniel Groves — 2008

Publications Mathématiques de l'IHÉS

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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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

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