Orbit Equivalence and actions of F_n

TL;DR

This paper demonstrates that there are uncountably many orbit inequivalent free actions of free groups on a standard probability space, highlighting the vast diversity of such actions.

Contribution

It establishes the existence of uncountably many orbit inequivalent free actions of F_n, expanding understanding of their classification in ergodic theory.

Findings

Uncountably many orbit inequivalent free actions of F_n.

Existence of 'E_0 many' such actions.

Diversity of free group actions on probability spaces.

Abstract

In this paper we show that there are "E_0 many" orbit inequivalent free actions of the free groups F_n, $2\leq n\leq\infty$, by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions.