MathAudit

Paper metadata

Original submission
October 16, 2024
Latest revision
August 19, 2026 · version 2
Claimed MSC
37B02, 37A35, 22B05, 20C07
arXiv categories
math.DS, math.AC, math.GN, math.GR
Comments
Some improvements are updated. The paper has been published on Discrete Contin. Dyn. Syst. Ser. S

Abstract

We investigate the dynamical property of the naive mean dimension for continuous actions of any countable group on compact metrizable spaces. It is shown that naive mean dimension serves as an upper bound of sofic mean dimension for actions of nonamenable groups. For algebraic actions we obtain more satisfactory results by looking at the naive version of mean rank for modules over integral group rings. We also consider the naive metric mean dimension and investigate its relations with sofic metric mean dimension.

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