Self-simulability of graph products
Group Theory
2026-05-27 v2 Dynamical Systems
Abstract
A group is self-simulable if all its computable actions admit SFT covers, which means roughly that they can be implemented with finitely many tiling constraints. We prove that a graph product of infinite finitely-generated groups is self-simulable if and only if its defining graph has no disconnecting clique consisting of amenable groups. In particular, a right-angled Artin group (a.k.a.\ a graph group) is self-simulable if and only if the defining graph has no disconnecting clique. As an application, we obtain that a graph product of infinite finitely-generated groups splits over an amenable subgroup if and only if the graph has a disconnecting clique consisting of amenable groups.
Cite
@article{arxiv.2605.20945,
title = {Self-simulability of graph products},
author = {Kanéda Blot and Ville Salo},
journal= {arXiv preprint arXiv:2605.20945},
year = {2026}
}
Comments
23 pages, 3 figures; v2 adds some geometric corollaries