Computing JSJ decompositions of hyperbolic groups

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Abstract

We present an algorithm that computes Bowditch's canonical JSJ decomposition of a given one‐ended hyperbolic group over its virtually cyclic subgroups. The algorithm works by identifying topological features in the boundary of the group. As a corollary we also show how to compute the JSJ decomposition of such a group over its virtually cyclic subgroups with infinite centre. We also give a new algorithm that determines whether a given one‐ended hyperbolic group is virtually Fuchsian. Our approach uses only the geometry of large balls in the Cayley graph and avoids Makanin's algorithm.
Original languageEnglish
Pages (from-to)527-558
Number of pages32
JournalJournal of Topology
Volume11
Issue number2
Early online date2 May 2018
DOIs
Publication statusPublished - Jun 2018

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