Local mean dimension theory for sofic group actions
Felipe García-Ramos
Uniwersytet Jagielloński, Kraków, Poland; Universidad Autónoma de San Luis Potosí, San Luis Potosí, MexicoYonatan Gutman
Polish Academy of Sciences, Warszawa, Poland

Abstract
Using a local perspective, we introduce mean dimension pairs and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group 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 , the full -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 .
Cite this article
Felipe García-Ramos, Yonatan Gutman, Local mean dimension theory for sofic group actions. Groups Geom. Dyn. (2025), published online first
DOI 10.4171/GGD/862