On the complexity of topological conjugacy of Toeplitz subshifts

被引：0
作者：
Marcin Sabok
Todor Tsankov
机构：
[1] McGill University,Department of Mathematics and Statistics
[2] Polish Academy of Sciences,Institute of Mathematics
[3] Université Paris Diderot,Institut de Mathématiques de Jussieu–PRG
来源：
Israel Journal of Mathematics | 2017年 / 220卷
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摘要：
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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页码：583 / 603
页数：20
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共 31 条
  • [1] Clemens J. D.(2009)Isomorphism of subshifts is a universal countable Borel equivalence relation Israel Journal of Mathematics 170 113-123
  • [2] Connes A.(1981)An amenable equivalence relation is generated by a single transformation Ergodic Theory and Dynamical Systems 1 431-450
  • [3] Feldman J.(2008)G-odometers and their almost one-to-one extensions Journal of the London Mathematical Society 78 1-20
  • [4] Weiss B.(2014)Invariant measures and orbit equivalence for generalized Toeplitz subshifts, Groups, Geometry and Dynamics 8 1007-1045
  • [5] Cortez M. I.(1994)The structure of hyperfinite Borel equivalence relations Transactions of the American Mathematical Society 341 193-225
  • [6] Petite S.(1995)A criterion for Toeplitz flows to be topologically isomorphic and applications Colloquium Mathematicum 68 219-228
  • [7] Cortez M. I.(1991)The Choquet simplex of invariant measures for minimal flows Israel Journal of Mathematics 74 241-256
  • [8] Petite S.(1999)Full groups of Cantor minimal systems Israel Journal of Mathematics 111 285-320
  • [9] Dougherty R.(2008)Non-treeability for product group actions Israel Journal of Mathematics 163 383-409
  • [10] Jackson S.(2002)Countable Borel equivalence relations Journal of Mathematical Logic 2 1-80
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