# Realizations of countable Borel equivalence relations

@inproceedings{Frisch2019RealizationsOC, title={Realizations of countable Borel equivalence relations}, author={Joshua Frisch and Alexander S. Kechris and Forte Shinko and Zolt'an Vidny'anszky}, year={2019} }

We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties. Some examples include minimal realizations on any perfect Polish space, realizations as Kσ relations, and realizations by continuous actions on the Baire space. We also consider questions related to realizations of specific important equivalence relations, like Turing and arithmetical equivalence. We focus in… Expand

#### 2 Citations

LECTURE NOTES: AN INTRODUCTION TO COUNTABLE BOREL EQUIVALENCE RELATIONS AND ACTIONS OF COUNTABLE GROUPS

- 2019

Borel measurable actions of countable groups have been intensively studied in the last decades from the viewpoints of descriptive set theory, dynamics and measured group theory [Gab10, Eps08, CM17,… Expand

Lifts of Borel actions on quotient spaces.

- Mathematics
- 2020

Given a countable Borel equivalence relation E and a countable group G, we study the problem of when a Borel action of G on X/E can be lifted to a Borel action of G on X.

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