THE COMPLEXITY OF THE TOPOLOGICAL CONJUGACY PROBLEM FOR TOEPLITZ SUBSHIFTS

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Kaya B.

ISRAEL JOURNAL OF MATHEMATICS, vol.220, no.2, pp.873-897, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 220 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s11856-017-1537-4
  • Journal Name: ISRAEL JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.873-897
  • Middle East Technical University Affiliated: Yes

Abstract

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.