Weakly and Strongly Aperiodic Subshifts of Finite Type on Baumslag-Solitar Groups

04/06/2020

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by   Julien Esnay, et al.

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We study the periodicity of subshifts of finite type (SFT) on Baumslag-Solitar groups. We show that for residually finite Baumslag-Solitar groups there exist both strongly and weakly-but-not-strongly aperiodic SFTs. In particular, this shows that unlike ℤ^2, but as ℤ^3, the notions of strong and weak periodicity are different for residually finite BS groups. More precisely, we prove that the weakly aperiodic SFT on BS(m,n) presented by Aubrun and Kari is in fact strongly aperiodic on BS(1,n). In addition, we exhibit an SFT which is weakly but not strongly aperiodic on BS(1,n). Finally, we show that there exists a strongly aperiodic SFT on BS(n,n).