On Polish groups admitting non-essentially countable actions

Autor:	Kechris, Alexander S., Malicki, Maciej, Panagiotopoulos, Aristotelis, Zielinski, Joseph
Rok vydání:	2019
Předmět:	Mathematics - Logic Mathematics - Dynamical Systems Primary 03E15 Secondary 54H20 22D05
Zdroj:	Ergod. Th. Dynam. Sys. 42 (2022) 180-194
Druh dokumentu:	Working Paper
DOI:	10.1017/etds.2020.133
Popis:	It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.08110 Zobrazit plný text záznamu View this record from Arxiv