On Braid Groups, Free Groups, and the Loop Space of the 2-Sphere

Abstract

The purpose of this article is to describe a connection between the single loop space of the 2-sphere, Artin’s braid groups, a choice of simplicial group whose homotopy groups are given by modules called Lie(n), as well as work of Milnor [17, 18], and Habegger-Lin [11, 15] on “homotopy string links”. The novelty of the current article is a description of connections between these topics.