Higher generation for pure braid groups

TL;DR

This paper introduces new families of highly generating subgroups within pure braid groups, utilizing geometric complexes like the restricted arc complex and dangling braiges to explore their structure.

Contribution

It presents novel constructions of highly generating subgroups in pure braid groups using geometric and combinatorial methods.

Findings

Identification of subgroups with high generating properties

Use of restricted arc complex in subgroup construction

Introduction of dangling braiges as a tool

Abstract

We exhibit some families of subgroups of the pure braid group that are highly generating, in the sense of Abels and Holz. In one class of examples, the relevant geometric object is a complex termed the restricted arc complex of a surface. Another arises by considering "dangling braiges," introduced by Bux, Fluch, Schwandt, Witzel and the author.