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.

arXiv comment39 pages, 7 figures, v2: accepted version, Canad. J. Math

References in corpus (12)

• Higher Dimensional Thompson Groups
• Stabilization for mapping class groups of 3-manifolds
• The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
• The braided Ptolemy-Thompson group is finitely presented
• The braided Thompson's groups are of type $F_{\infty }$
• The Brin-Thompson groups sV are of type F_\infty
• Thompson groups for systems of groups, and their finiteness properties
• Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
• Almost-automorphisms of trees, cloning systems and finiteness properties
• Classifying spaces from Ore categories with Garside families
• 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