Topo-isomorphisms of irregular Toeplitz subshifts for residually finite groups

Abstract

For every countable residually finite group $G$ and every totally disconnected metric compactification $\overleftarrow{G}$ of $G$, we construct an irregular Toeplitz subshift $X\subseteq \{0,1{\}}^G$ whose maximal equicontinuous factor is $\overleftarrow{G}$ and such that $X$ is a topo-isomorphic extension of $\overleftarrow{G}$. When the acting group $G$ is amenable, our construction yields new examples of mean-equicontinuous dynamical systems.