The nonexistence of expansive actions on Suslinian continua by groups of subexponential growth

TL;DR

This paper proves that groups with subexponential growth cannot have expansive actions on Suslinian continua, revealing limitations on the dynamical complexity such groups can exhibit.

Contribution

It establishes a nonexistence result for expansive group actions on Suslinian continua for groups of subexponential growth.

Findings

Groups of subexponential growth cannot act expansively on Suslinian continua.

Provides a new restriction on dynamical systems involving such groups and continua.

Enhances understanding of the interplay between group growth and topological dynamics.

Abstract

We show that if $G$ is a finitely generated group of subexponential growth and $X$ is a Suslinian continuum, then any action of $G$ on $X$ cannot be expansive.