Homological stability for the ribbon Higman--Thompson groups
Abstract
We generalize the notion of asymptotic mapping class groups and allow them to surject to the Higman--Thompson groups, answering a question of Aramayona and Vlamis in the case of the Higman--Thompson groups. When the underlying surface is a disk, these new asymptotic mapping class groups can be identified with the ribbon and oriented ribbon Higman--Thompson groups. We use this model to prove that the ribbon Higman--Thompson groups satisfy homological stability, providing the first homological stability result for dense subgroups of big mapping class groups. Our result can also be treated as an extension of Szymik--Wahl's work on homological stability for the Higman--Thompson groups to the surface setting.
Cite
@article{arxiv.2106.08751,
title = {Homological stability for the ribbon Higman--Thompson groups},
author = {Rachel Skipper and Xiaolei Wu},
journal= {arXiv preprint arXiv:2106.08751},
year = {2025}
}
Comments
23 pages; split off from arXiv:2103.14589v1 with the first part available as arXiv:2103.14589v2;v3, many improvements, to appear in Algebr. Geom. Topol