Finiteness properties for relatives of braided Higman–Thompson groups

We study the finiteness properties of the braided Higman–Thompson group bV_{d,r}(H) with labels in H\leq B_d , and bF_{d,r}(H) and bT_{d,r}(H) with labels in H\leq PB_d , where B_d is the braid group with d strings and PB_d is its pure braid subgroup. We show that for all d\geq 2 and r\geq 1 , the g...

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Bibliographic Details
Published in:Groups, geometry and dynamics geometry and dynamics, 2023-01, Vol.17 (4), p.1357-1391
Main Authors: Skipper, Rachel, Wu, Xiaolei
Format: Article
Language:English
Subjects:
Algebraic topology
Group theory
Mathematical research
Topology
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Summary:We study the finiteness properties of the braided Higman–Thompson group bV_{d,r}(H) with labels in H\leq B_d , and bF_{d,r}(H) and bT_{d,r}(H) with labels in H\leq PB_d , where B_d is the braid group with d strings and PB_d is its pure braid subgroup. We show that for all d\geq 2 and r\geq 1 , the group bV_{d,r}(H) (resp. bT_{d,r}(H) or bF_{d,r}(H) ) is of type F_n if and only if H is. Our result in particular confirms a recent conjecture of Aroca and Cumplido.
ISSN:1661-7207
1661-7215
DOI:10.4171/ggd/731