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

Giles Gardam; Dawid Kielak; Alan Logan

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

Giles Gardam, Dawid Kielak, Alan Logan

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Publication status	Accepted/In press - 17 Oct 2025

Access to Document

Download pdf
Paper accepted for publication. Logan, A., Gardam, G. & Kielak, D., " JSJ decompositions and polytopes for two-generator one-relator groups", Mathematical Proceedings of the Cambridge Philosophical Society, Vol??, Iss??, pg??? (2025). Cambridge University Press. DOI:???
Accepted author manuscript, 623 KBLicence: CC BY-NC-ND

Cite this

@article{293b7fb9864047d6bc2f3fb770e7b123,

title = "JSJ decompositions and polytopes for two-generator one-relator groups",

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.",

author = "Giles Gardam and Dawid Kielak and Alan Logan",

year = "2025",

month = oct,

day = "17",

language = "English",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - JSJ decompositions and polytopes for two-generator one-relator groups

AU - Gardam, Giles

AU - Kielak, Dawid

AU - Logan, Alan

PY - 2025/10/17

Y1 - 2025/10/17

N2 - 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.

AB - 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.

M3 - Article

SN - 0305-0041

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -

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

Abstract

Access to Document

Fingerprint

Cite this