%0 Journal Article
%T On the complexity of topological conjugacy of Toeplitz subshifts
%A Marcin Sabok
%A Todor Tsankov
%J Mathematics
%D 2015
%I arXiv
%X In this paper, we study the descriptive set theoretic complexity of the equivalence relation of conjugacy of Toeplitz subshifts of a residually finite group $G$. On the one hand, we show that if $G = \mathbb{Z}$, then topological conjugacy on Toeplitz subshifts with separated holes is amenable. In contrast, if $G$ is non-amenable, then conjugacy of Toeplitz $G$-subshifts is a non-amenable equivalence relation. The results were motivated by a general question, asked by Gao, Jackson and Seward, about the complexity of conjugacy for minimal, free subshifts of countable groups.
%U http://arxiv.org/abs/1506.07671v1