Braiding groups of automorphisms and almost-automorphisms of trees

Abstract

We introduce "braided" versions of self-similar groups and Röver--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar groups are what we call "self-identical". In particular we use a braided version of the Grigorchuk group to construct a new group called the braided Röver group, which we prove is of type $F_{\infty }$. Our techniques involve using so called $d$-ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties.

39 pages, 7 figures, v2: accepted version, Canad. J. Math

References in corpus (3)

• Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
• Most big mapping class groups fail the Tits Alternative
• Braided Brin-Thompson Groups

Cited by in corpus (1)

• Braided Thompson groups with and without quasimorphisms