# Strongly Aperiodic SFTs on Generalized Baumslag-Solitar groups

1 GALaC - Graphes, Algorithmes et Combinatoire
LISN - Laboratoire Interdisciplinaire des Sciences du Numérique, AAC - Algorithmes, Apprentissage et Calcul
Abstract : We look at constructions of aperiodic 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 first a structural theorem by Whyte and second 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03649781
Contributor : Nicolas Bitar Connect in order to contact the contributor
Submitted on : Friday, April 22, 2022 - 11:05:56 PM
Last modification on : Friday, August 5, 2022 - 2:58:08 PM

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• HAL Id : hal-03649781, version 1

### Citation

Nathalie Aubrun, Nicolás Bitar, Sacha Huriot-Tattegrain. Strongly Aperiodic SFTs on Generalized Baumslag-Solitar groups. 2022. ⟨hal-03649781⟩

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