The Isomorphism Problem for Toral Relatively Hyperbolic Groups

Details The Isomorphism Problem for Toral Relatively Hyperbolic Groups The Isomorphism Problem for Toral Relatively Hyperbolic Groups

2005-12-27

arxiv.org/abs/math/0512605v3

Publ. Math., Inst. Hautes Etudes Sci. 107 no.1 (2008) 211-290.

Mathematics

Group Theory

Version 3 is 90 pages (the increased length is due mostly to typesetting). Lots of rewriting due to referee's comments. Public

Scientific paper

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); and (ii) fully residually free groups (Bumagin, Kharlampovich and Miasnikov). 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.

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