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Finiteness properties for relatives of braided Higman-Thompson groups

被引：2
|
作者：
Skipper, Rachel [1 ]
Wu, Xiaolei [2 ]
机构：
[1] Ecole Normale Super, Dept Math & Applicat, 45 Rue Ulm, F-75005 Paris, France
[2] Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200438, Peoples R China
来源：
GROUPS GEOMETRY AND DYNAMICS | 2023年 / 17卷 / 04期
关键词：
Braided Higman-Thompson groups; ribbon Higman-Thompson groups; topological finiteness properties; MAPPING CLASS-GROUPS; HOMOLOGY; SUBGROUPS; STABILITY;
D O I：
10.4171/GGD/731
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 <= PBd, where B-d 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 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.
引用
收藏
页码：1357 / 1391
页数：35
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