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arXiv · 2106.08751

Homological stability for the ribbon Higman--Thompson groups

Rachel Skipper·Xiaolei Wu
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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.

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BibTeXRIS

Rachel Skipper, Xiaolei Wu. 2023-11-24. Homological stability for the ribbon Higman--Thompson groups. https://doi.org/10.2140/agt.2025.25.4633

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