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 language | English |
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Pages (from-to) | 527-558 |
Number of pages | 32 |
Journal | Journal of Topology |
Volume | 11 |
Issue number | 2 |
Early online date | 2 May 2018 |
DOIs | |
Publication status | Published - 1 Jun 2018 |