  The purpose of this article is to describe connections between the 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,
and Habegger-Lin on "homotopy string links". The current article exploits Lie
algebras associated to Vassiliev invariants in work of T. Kohno, and provides
connections between these various topics.
  Two consequences are as follows:
  1) the homotopy groups of spheres are identified as "natural" sub-quotients
of free products of pure braid groups, and
  2) an axiomatization of certain simplicial groups arising from braid groups
is shown to characterize the homotopy types of connected $CW$-complexes.
