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Asymptotic dimension and hyperfiniteness of generic Cantor actions

  • Sumun Iyer

    Carnegie Mellon University, Pittsburgh, USA
    ORCID

  • Forte Shinko

    University of California, Berkeley, USA
    ORCID
Asymptotic dimension and hyperfiniteness of generic Cantor actions cover

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Abstract

We show that for a countable discrete group which is locally of finite asymptotic dimension, the generic continuous action on Cantor space has hyperfinite orbit equivalence relation. In particular, this holds for free groups, answering a question of Frisch–Kechris–Shinko–Vidnyánszky.

Cite this article

Sumun Iyer, Forte Shinko, Asymptotic dimension and hyperfiniteness of generic Cantor actions. Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/896