The complexity of topological conjugacy of pointed Cantor minimal systems

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Kaya B.

ARCHIVE FOR MATHEMATICAL LOGIC, vol.56, pp.215-235, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56
  • Publication Date: 2017
  • Doi Number: 10.1007/s00153-017-0534-y
  • Journal Name: ARCHIVE FOR MATHEMATICAL LOGIC
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.215-235
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation Delta(+)(R) on R-N defined by x Delta(+)(R)y double left right arrow {x(i):i is an element of N} = {y(i):i is an element of N}. Moreover, we show that Delta(+)(R) is a lower bound for the Borel complexity of topological conjugacy of Cantor minimal systems. Finally, we interpret our results in terms of properly ordered Bratteli diagrams and discuss some applications.