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Strongly Aperiodic SFTs on Generalized Baumslag-Solitar groups

04/25/2022
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by   Nathalie Aubrun, et al.
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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 𝔽_n×ℤ and BS(m,n) of our own. Our two constructions rely on a path-folding technique that lifts an SFT on ℤ^2 inside an SFT on 𝔽_n×ℤ or an SFT on the hyperbolic plane inside an SFT on BS(m,n). In the case of 𝔽_n×ℤ the path folding technique also preserves minimality, so that we get minimal strongly aperiodic SFTs on unimodular GBS.

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