Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.20945 |
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Inhaltsangabe:
- 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.