Computing JSJ decompositions of hyperbolic groups
Geometric Topology
2018-05-08 v4 Group Theory
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 or not 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.
Keywords
Cite
@article{arxiv.1611.00652,
title = {Computing JSJ decompositions of hyperbolic groups},
author = {Benjamin Barrett},
journal= {arXiv preprint arXiv:1611.00652},
year = {2018}
}
Comments
38 pages, one figure. v4 corrects two spelling mistakes. This is the final version accepted by the Journal of Topology