JSJ decompositions and polytopes for two-generator one-relator groups
Abstract
Abstract We provide a direct connection between the script upper Z Subscript max Z max $\mathcal{Z}_{\max}$ (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 script upper Z Subscript max Z max $\mathcal{Z}_{\max}$ -JSJ decomposition of such groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Finite Group Theory Research
Advanced Algebra and Geometry
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 2
- Pages
- 1117–1147
- Publication date
- 11 May 2026
- Language
- EN