Homological stability for the ribbon Higman--Thompson groups

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 ident...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Skipper, Rachel, Wu, Xiaolei
Format: Article
Language:English
Subjects:
Asymptotic properties
Homology
Mapping
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422