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.

arXiv comment23 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

References in corpus (6)

• Stabilization for mapping class groups of 3-manifolds
• Big mapping class groups: an overview
• The homology of the Higman-Thompson groups
• Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
• The homology of Richard Thompson's group F
• Finiteness properties for relatives of braided Higman--Thompson groups

Cited by in corpus (1)

• Finiteness properties for relatives of braided Higman--Thompson groups