On the complexity of topological conjugacy of Toeplitz subshifts

2015/06/25 by Sabok, Marcin, Tsankov, Todor · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1506.07671

Abstract

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 = 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.

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