Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braid groups, free groups, and the loop space of the 2-sphere   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.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph