Weak density of orbit equivalence classes of free group actions

TL;DR

This paper proves that the orbit-equivalence class of any essentially free, measure-preserving action of a free group is densely approximated by other actions in the space of all such actions.

Contribution

It establishes the weak density of orbit-equivalence classes for free group actions, advancing understanding of their classification and approximation properties.

Findings

Orbit-equivalence classes are weakly dense in the space of free group actions.

Any essentially free, measure-preserving free group action can be approximated by others.

The result applies to actions of free groups on probability spaces.

Abstract

It is proven that the orbit-equivalence class of any essentially free probability-measure-preserving action of a free group $G$ is weakly dense in the space of actions of $G$.