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arXiv · 2605.20945

Self-simulability of graph products

Kanéda Blot·Ville Salo
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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 (algebraically, or in a certain geometric sense) over an amenable subgroup if and only if the graph has a disconnecting clique consisting of amenable groups.

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Kanéda Blot, Ville Salo. 2026-05-20. Self-simulability of graph products. https://arxiv.org/abs/2605.20945

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