Finiteness properties for relatives of braided Higman--Thompson groups

2021/03/24 by Skipper, Rachel, Wu, Xiaolei · 1 citation
#20F36 #20J05 #57M07 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2103.14589

Abstract

We study the finiteness properties of the braided Higman--Thompson group bV_d,r(H) with labels in H≤ B_d, and bF_d,r(H) and bT_d,r(H) with labels in H≤ 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≥ 2 and r≥ 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.

Cited by

• Stable homology of Higman--Thompson groups via scanning methods

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