Geodesic
Finiteness properties for relatives of braided Higman–Thompson groups
Rachel Skipper1 ; Xiaolei Wu2
1École Normale Supérieure, Paris, France
2Fudan University, Shanghai, China
Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1357-1391

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DOI

We study the finiteness properties of the braided Higman–Thompson group bVd,r​(H) with labels in H≤Bd​, and bFd,r​(H) and bTd,r​(H) with labels in H≤PBd​, where Bd​ is the braid group with d strings and PBd​ is its pure braid subgroup. We show that for all d≥2 and r≥1, the group bVd,r​(H) (resp. bTd,r​(H) or bFd,r​(H)) is of type Fn​ if and only if H is. Our result in particular confirms a recent conjecture of Aroca and Cumplido.
DOI : 10.4171/ggd/731
Classification : 20-XX, 57-XX
Mots-clés : Braided Higman–Thompson groups, ribbon Higman–Thompson groups, topological finiteness properties

Rachel Skipper  1   ; Xiaolei Wu  2

1 École Normale Supérieure, Paris, France
2 Fudan University, Shanghai, China 
Rachel Skipper; Xiaolei Wu. Finiteness properties for relatives of braided Higman–Thompson groups. Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1357-1391. doi: 10.4171/ggd/731
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     title = {Finiteness properties for relatives of braided {Higman{\textendash}Thompson} groups},
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