On braid groups and homotopy groups

TL;DR

This paper explores the relationships between braid groups, homotopy groups of the 2-sphere, and Lie algebras from pure braid groups, highlighting their connections and posing open questions.

Contribution

It provides an exposition of the connections between braid groups, homotopy groups, and Lie algebras, and discusses their implications and open problems.

Findings

Connections between braid groups and homotopy groups elucidated

Lie algebras from pure braid groups analyzed in context of Vassiliev invariants

Open questions proposed for further research

Abstract

This 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.