Year: 2004
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Cohen, F. R., Wu, J.
Institutions: National University of Singapore, University of Rochester
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394640949