Morse and stable subgroups via the coset intersection complex

TL;DR

This paper explores the relationship between Morse and stable subgroups within the coset intersection complex framework, proving that under certain conditions, Morse subgroups are stable, with applications to specific groups.

Contribution

It establishes conditions under which Morse subgroups are stable in the coset intersection complex, extending known results to new classes of groups.

Findings

Infinite-index Morse subgroups are stable under certain conditions.

Main theorem recovers results for right-angled Artin groups and graph products.

Genus-two handlebody group has all infinite-index Morse subgroups stable.

Abstract

In this note, we study the equivalence of Morse and stable subgroups in the framework of the coset intersection complex. Under certain conditions on a coset intersection complex of a group, we prove that infinite-index Morse subgroups are stable. Our main theorem recovers results in the literature on right-angled Artin groups and graph products. As an application, we show that for the genus-two handlebody group, any infinite-index Morse subgroup is stable.