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arXiv · 2401.08440

Local mean dimension theory for sofic group actions

Felipe García-Ramos·Yonatan Gutman
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Abstract

Using a local perspective, we introduce \textit{mean dimension pairs} and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group $G$ has positive mean dimension. In addition we show that the mean dimension map is Borel, and that the set of subshifts with completely positive mean dimension of $[0,1]^G$, the full $G$-shift on the interval, is a complete coanalytic set in the set of all subshifts (hence not Borel). Our results are new even when the acting group is $\Z$.

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Felipe García-Ramos, Yonatan Gutman. 2024-01-16. Local mean dimension theory for sofic group actions. https://arxiv.org/abs/2401.08440

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