Kanéda Blot | Searcharxiv

arXiv2026

A geometric obstruction to self-simulation for groups

We introduce a new quasi-isometry invariant for finitely generated groups and show that every group with this property admits a subshift which is effectively closed by patterns and that cannot be realized as the topological factor of any subshift of finite type. We provide several examples of groups with the property, such as amenable groups, multi-ended groups, generalized Baumslag-Solitar groups, fundamental groups of surfaces, and cocompact Fuchsian groups.

math.GR↗

arXiv2026

Self-simulability of graph products

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.

math.GR↗