Minimal subshifts of arbitrary mean topological dimension

TL;DR

This paper constructs minimal subshifts over group actions with any prescribed mean topological dimension below the polyhedron's dimension, expanding understanding of dynamical systems in topological dynamics.

Contribution

It introduces a method to construct minimal subshifts with arbitrary mean topological dimension less than the polyhedron's dimension for countable infinite amenable groups.

Findings

Constructed minimal subshifts with prescribed mean topological dimension

Demonstrated flexibility in mean topological dimension for subshifts

Extended the theory of topological dynamics in group actions

Abstract

Let $G$ be a countable infinite amenable group and $P$ be a polyhedron. We give a construction of minimal subshifts of $P^G$ with arbitrarily mean topological dimension less than $\dim P$.