JSJ decompositions and polytopes for two-generator one-relator groups

Giles Gardam, Dawid Kielak, Alan D. Logan

Published 2021-01-06Version 1

We provide a direct connection between the $\mathcal{Z}_{\max}$ (or essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic two-generator one-relator group with abelianisation of rank $2$. We deduce various structural and algorithmic properties, like the existence of a quadratic-time algorithm computing the $\mathcal{Z}_{\max}$-JSJ decomposition of such groups.