Braids and crossed modules

TL;DR

This paper presents a novel interpretation of Artin's braid group as a crossed module over itself, providing new insights into the algebraic structure of braids and their relations.

Contribution

It introduces a new perspective by describing the braid group as a crossed module, interpreting braid relations as structure relations within this framework.

Findings

Braid group modeled as a crossed module

Braid relations interpreted as structure relations

Provides a new algebraic perspective on braids

Abstract

We describe Artin's braid group on a (fixed) finite number of strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations.