Surface braid groups

Abstract

This project explored the solution to the word problem of braids over the 2-sphere as presented in [15, Theorem 3.1], in the hopes that it can be related to Brunnian braids and homotopy groups of spheres as introduced via the exact sequence in [10, Theorem 1.2]. It describes the process of Artin combing as the original solution to the word problem for braids over the disc by Artin[4] and introduces a new interpretation to the map φ : Brunn+1(S2) → Brunn(D2) in the exact sequence.