A combination theorem for the twist conjecture for Artin groups
Group Theory
2026-05-13 v2
Abstract
We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the isomorphism problem for Artin groups. Along the way we also prove a combination result for the ribbon property for vertices.
Cite
@article{arxiv.2507.13971,
title = {A combination theorem for the twist conjecture for Artin groups},
author = {Oli Jones and Giorgio Mangioni and Giovanni Sartori},
journal= {arXiv preprint arXiv:2507.13971},
year = {2026}
}
Comments
V2: Several improvements in the exposition; furthermore, points (2) and (3) of Corollary E now only deal with big chunks without separating edges. Updated to match the version published in Journal of Algebra. Now 35 pages, 7 figures. Comments are welcome!