Work

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

Year: 2026

Type: article

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.

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004126101959

Authors: GILES GARDAM, DAWID KIELAK, ALAN D. LOGAN

Institutions: University of Bonn, University of Oxford, Heriot-Watt University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: European Commission, Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council