A note on separability in outer automorphism groups

TL;DR

This paper provides a criterion for subgroup separability in outer automorphism groups, extending previous results on mapping class groups and answering open questions in the field.

Contribution

It introduces a new criterion for subgroup separability in outer automorphism groups, generalizing prior work on mapping class groups.

Findings

Established a criterion for subgroup separability in outer automorphism groups.

Extended and strengthened previous results on mapping class groups.

Addressed open questions posed by Hagen and Sisto.

Abstract

We give a criterion for separability of subgroups of certain outer automorphism groups. This answers questions of Hagen and Sisto, by strengthening and generalizing a result of theirs on mapping class groups.