𝜎-lacunary actions of Polish groups

Grebík, Jan

doi:10.1090/proc/14982

$\sigma$-lacunary actions of Polish groups
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by Jan Grebík PDF

Proc. Amer. Math. Soc. 148 (2020), 3583-3589 Request permission

Abstract:

We show that every essentially countable orbit equivalence relation induced by a continuous action of a Polish group on a Polish space is $\sigma$-lacunary. In combination with Gao and Jackson [Invent. Math. 201 (2015), pp. 309–383] we obtain a straightforward proof of the result from Ding and Gao [Adv. Math. 307 (2017), pp. 312–343] that every essentially countable equivalence relation that is induced by an action of an abelian nonarchimedean Polish group is Borel reducible to $\mathbb {E}_0$, i.e., it is essentially hyperfinite.

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