sigma-lacunary actions of Polish groups

0525501 - MÚ 2021 RIV US eng J - Journal Article
Grebík, Jan
sigma-lacunary actions of Polish groups.
Proceedings of the American Mathematical Society. Roč. 148, č. 8 (2020), s. 3583-3589. ISSN 0002-9939. E-ISSN 1088-6826
R&D Projects: GA ČR GF17-33849L
Institutional support: RVO:67985840
Keywords : Polish group * Polish space
OECD category: Pure mathematics
Impact factor: 1.016, year: 2020
Method of publishing: Limited access
https://doi.org/10.1090/proc/14982

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 E-0, i.e., it is essentially hyperfinite.
Permanent Link: http://hdl.handle.net/11104/0309617