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Publication - Dr Benjamin Barrett

    Computing JSJ decompositions of hyperbolic groups

    Citation

    Barrett, B, 2018, ‘Computing JSJ decompositions of hyperbolic groups’. Journal of Topology, vol 11., pp. 527-558

    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.

    Full details in the University publications repository