# The automorphism groups of the profinite braid groups

## TL;DR

This paper determines the automorphism groups of profinite braid groups with four or more strings using the profinite Grothendieck-Teichmüller group, advancing understanding of their algebraic symmetries.

## Contribution

It explicitly describes the automorphism groups of these braid groups in terms of the profinite Grothendieck-Teichmüller group, a novel connection.

## Key findings

- Automorphism groups characterized for profinite braid groups with ≥4 strings.
- Established a link between automorphisms and the profinite Grothendieck-Teichmüller group.
- Enhanced understanding of algebraic symmetries in braid groups.

## Abstract

In this paper we determine the automorphism groups of the profinite braid groups with four or more strings in terms of the profinite Grothendieck-Teichm\"uller group.