2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225926This article is an exposition of certain connections between the braid groups, classical homotopy groups of the 2-sphere, as well as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invariants of pure braids. Natural related questions are posed at the end of this article.This is the version published by Geometry & Topology Monographs on 22 February 2008Algebraic TopologyGroup Theory20F36, 55Q40, 18G30, 20F40, 55U10text