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arXiv · 2409.03078

Asymptotic dimension and hyperfiniteness of generic Cantor actions

Sumun Iyer·Forte Shinko
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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-Vidny\'anszky.

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Sumun Iyer, Forte Shinko. 2024-09-04. Asymptotic dimension and hyperfiniteness of generic Cantor actions. https://arxiv.org/abs/2409.03078

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