The complexity of the topological conjugacy problem for Toeplitz subshifts

Research paper by Burak Kaya

Indexed on: 03 Mar '16Published on: 03 Mar '16Published in: Mathematics - Logic


In this paper, we analyze the Borel complexity of the topological conjugacy relation on Toeplitz subshifts. More specifically, we prove that topological conjugacy of Toeplitz subshifts with separated holes is hyperfinite. Indeed, we show that the topological conjugacy relation is hyperfinite on a larger class of Toeplitz subshifts which we call Toeplitz subshifts with growing blocks. This result provides a partial answer to a question asked by Sabok and Tsankov.