Strongly aperiodic SFTs on hyperbolic groups: where to find them and why we love them

Rieck, Yo'av

doi:10.33044/revuma.3155

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Subshifts and Aperiodicity1

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2023

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“…It is strongly aperiodic if all its configurations have trivial stabilizer. For a recent survey on the existence of strongly aperiodic SFTs, we refer to [45].…”

Section: Subshifts and Aperiodicitymentioning

confidence: 99%

Strongly aperiodic SFTs on generalized Baumslag–Solitar groups

Aubrun¹,

Bitar²,

Huriot-Tattegrain³

2023

Ergod. Th. Dynam. Sys.

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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.

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“…It is strongly aperiodic if all its configurations have trivial stabilizer. For a recent survey on the existence of strongly aperiodic SFTs, we refer to [45].…”

Section: Subshifts and Aperiodicitymentioning

confidence: 99%