Work

The isomorphism problem for toral relatively hyperbolic groups

Year: 2008

Type: article

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special cases we recover solutions to the isomorphism problem for: (i) torsion-free hyperbolic groups (Sela, [60] and unpublished); and (ii) finitely generated fully residually free groups (Bumagin, Kharlampovich and Miasnikov [14]).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

Source: Publications mathématiques de l IHÉS

DOI: 10.1007/s10240-008-0014-3

Authors: François Dahmani, Daniel Groves

Institutions: Université Toulouse III - Paul Sabatier, Institut de Mathématiques de Toulouse, University of Illinois Chicago

Language: French

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,590

Funder: Agence Nationale de la Recherche