JSJ decompositions and polytopes for two-generator one-relator groups
Group Theory
2025-10-22 v3 Algebraic Topology
Abstract
We provide a direct connection between the Z_{max} (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianisation of rank . We deduce various structural and algorithmic properties, like the existence of a quadratic-time algorithm computing the Z_{max}-JSJ decomposition of such groups.
Cite
@article{arxiv.2101.02193,
title = {JSJ decompositions and polytopes for two-generator one-relator groups},
author = {Giles Gardam and Dawid Kielak and Alan D. Logan},
journal= {arXiv preprint arXiv:2101.02193},
year = {2025}
}
Comments
41 pages. Final version accepted for publication