Homological stability for the ribbon Higman–Thompson groups

Skipper, Rachel; Wu, Xiaolei

doi:10.2140/agt.2025.25.4633

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Homological stability for the ribbon Higman–Thompson groups

Rachel Skipper and Xiaolei Wu

Algebraic & Geometric Topology 25 (2025) 4633–4665

DOI: 10.2140/agt.2025.25.4633

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 and Wahl’s work on homological stability for the Higman–Thompson groups to the surface setting.

Keywords

braided Higman–Thompson groups, ribbon Higman–Thompson groups, asymptotic mapping class groups, big mapping class groups, finiteness property, homological stability

Mathematical Subject Classification

Primary: 19D23, 20F36, 20J05, 57M07

References

Publication

Received: 31 December 2022

Revised: 23 October 2023

Accepted: 19 November 2023

Published: 20 November 2025

Authors

Rachel Skipper
Department of Mathematics University of Utah Salt Lake City, UT United States

Xiaolei Wu
Shanghai Center for Mathematical Sciences Fudan University Shanghai China

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Volume 25, issue 8 (2025)