Integrable orbit equivalence rigidity for free groups

TL;DR

This paper proves that accessible groups orbit equivalent to free groups are virtually free and that such equivalences extend to their end compactifications, revealing rigidity properties of free groups.

Contribution

It establishes integrable orbit equivalence rigidity for free groups and extends these equivalences to their end compactifications, advancing understanding of group orbit structures.

Findings

Accessible groups orbit equivalent to free groups are virtually free.

Integrable orbit equivalences extend to end compactifications.

Rigidity results for free groups under orbit equivalence.

Abstract

It is shown that every accessible group which is integrable orbit equivalent to a free group is virtually free. Moreover, we also show that any integrable orbit-equivalence between finitely generated groups extends to their end compactifications.