A new family of infinitely braided Thompson's groups

Abstract

We present a generalization of the Dehornoy-Brin braided Thompson group $B{V}_2$ that uses recursive braids. Our new groups are denoted by $B{V}_{n,r}(H)$, for all $n\ge 2,r\ge 1$ and $H\le {\mathcal{B}}_n$, where ${\mathcal{B}}_n$ is the braid group on $n$ strands. We give a new approach to deal with braided Thompson groups by using strand diagrams. We show that $B{V}_{n,r}(H)$ is finitely generated if $H$ is finitely generated.

25 pages, 19 figures