Corpus ID: 235446293

Finiteness properties for relatives of braided Higman--Thompson groups

@inproceedings{Skipper2021FinitenessPF,
  title={Finiteness properties for relatives of braided Higman--Thompson groups},
  author={Rachel Skipper and Xiaolei Wu},
  year={2021}
}
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. 
1 Citations
Homological stability for the ribbon Higman--Thompson groups
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–ThompsonExpand

References

SHOWING 1-10 OF 40 REFERENCES
Finiteness properties of soluble arithmetic groups over global function fields
Let G be a Chevalley group scheme and B < G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O S be the correspondingExpand
Braided Brin-Thompson Groups
We construct braided versions sVbr of the Brin-Thompson groups sV and prove that they are of type F∞. The proof involves showing that the matching complexes of colored arcs on surfaces are highlyExpand
Homological stability for the ribbon Higman--Thompson groups
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–ThompsonExpand
A new family of infinitely braided Thompson's groups
We present a generalization of the Dehornoy-Brin braided Thompson group $BV_2$ that uses recursive braids. Our new groups are denoted by $BV_{n,r}(H)$, for all $n\geq 2,r\geq 1$ and $H \leqExpand
Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the braidedExpand
Twisted Brin-Thompson groups
We construct a family of infinite simple groups that we call \emph{twisted Brin-Thompson groups}, generalizing Brin's higher-dimensional Thompson groups $sV$ ($s\in\mathbb{N}$). We use twistedExpand
Almost-automorphisms of trees, cloning systems and finiteness properties
We prove that the group of almost-automorphisms of the infinite rooted regular $d$-ary tree $\mathcal{T}_d$ arises naturally as the Thompson-like group of a so called $d$-ary cloning system. AExpand
Classifying spaces from Ore categories with Garside families
We describe how an Ore category with a Garside family can be used to construct a classifying space for its fundamental group(s). The construction simultaneously generalizes Brady's classifying spaceExpand
Simple groups separated by finiteness properties
We show that for every positive integer n there exists a simple group that is of type $$\mathrm {F}_{n-1}$$Fn-1 but not of type $$\mathrm {F}_n$$Fn. For $$n\ge 3$$n≥3 these groups are the first knownExpand
Röver's simple group is of type F ∞
We prove that Claas Rover's Thompson-Grigorchuk simple group V G has type F∞. The proof involves constructing two complexes on which V G acts: a simplicial complex analogous to the Stein complex forExpand
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