A geometric obstruction to self-simulation for groups
Group Theory
2025-10-14 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.2510.10291,
title = {A geometric obstruction to self-simulation for groups},
author = {Sebastián Barbieri and Kanéda Blot and Mathieu Sablik and Ville Salo},
journal= {arXiv preprint arXiv:2510.10291},
year = {2025}
}
Comments
23 pages, 5 pictures from out of this world