Measure equivalence classification of right-angled Artin groups: the finite $\mathrm{Out}$ classes

TL;DR

This paper classifies right-angled Artin groups with finite outer automorphism groups based on their measure and orbit equivalence classes, providing a comprehensive understanding of their classification.

Contribution

It establishes a measure equivalence classification for right-angled Artin groups with finite outer automorphism groups, a novel result in geometric group theory.

Findings

Identifies measure equivalence classes for these groups

Determines orbit equivalence relations among them

Provides a classification framework for such groups

Abstract

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$.