Morse and stable subgroups via the coset intersection complex
Group Theory
2026-04-01 v1
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.
Keywords
Cite
@article{arxiv.2603.29158,
title = {Morse and stable subgroups via the coset intersection complex},
author = {Tomohiro Fukaya and Haoyang He and Eduardo Martínez-Pedroza and Takumi Matsuka},
journal= {arXiv preprint arXiv:2603.29158},
year = {2026}
}
Comments
v1: 7 pages