# Weak density of orbit equivalence classes and free products of infinite abelian groups

## TL;DR

This paper proves that for free products of infinite abelian groups, the orbit equivalence classes of their free p.m.p. actions are densely distributed, extending previous results known for free groups.

## Contribution

It extends Bowen's result by showing weak density of orbit equivalence classes for free products of infinite abelian groups.

## Key findings

- Orbit equivalence classes are weakly dense in the space of p.m.p. actions.
- Extension of Bowen's result from free groups to free products of infinite abelian groups.
- Applicable to all free, probability-measure-preserving actions of such groups.

## Abstract

We show that if a countable group $G$ is the free product of infinite abelian groups, then for every free, probability-measure-preserving (p.m.p.) action of $G$, its orbit equivalence class is weakly dense in the space of p.m.p. actions of $G$. This extends Lewis Bowen's result for free groups.