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<p>We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit moreover to show that every such action has finite Borel asymptotic dimension.</p>

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Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月29日

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  • Petr Naryshkin,
  • Andrea Vaccaro

摘要

We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit moreover to show that every such action has finite Borel asymptotic dimension.