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Journal Articles Ergodic Theory and Dynamical Systems Year : 2023

Strongly aperiodic SFTs on generalized Baumslag–Solitar groups

Abstract

Abstract We look at constructions of aperiodic subshifts of finite type (SFTs) on fundamental groups of graph of groups. In particular, we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by Whyte and on two constructions of strongly aperiodic SFTs on $\mathbb {F}_n\times \mathbb {Z}$ and $BS(m,n)$ of our own. Our two constructions rely on a path-folding technique that lifts an SFT on $\mathbb {Z}^2$ inside an SFT on $\mathbb {F}_n\times \mathbb {Z}$ or an SFT on the hyperbolic plane inside an SFT on $BS(m,n)$ . In the case of $\mathbb {F}_n\times \mathbb {Z}$ , the path folding technique also preserves minimality, so that we get minimal strongly aperiodic SFTs on unimodular GBS groups.

Dates and versions

hal-04284393 , version 1 (14-11-2023)

Identifiers

Cite

Nathalie Aubrun, Nicolás Bitar, Sacha Huriot-Tattegrain. Strongly aperiodic SFTs on generalized Baumslag–Solitar groups. Ergodic Theory and Dynamical Systems, 2023, pp.1-30. ⟨10.1017/etds.2023.44⟩. ⟨hal-04284393⟩
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