Local mean dimension theory for sofic group actions

  • Felipe García-Ramos

    Uniwersytet Jagielloński, Kraków, Poland; Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
  • Yonatan Gutman

    Polish Academy of Sciences, Warszawa, Poland
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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