Grup de trenes i el teorema d’Alexander

Abstract

[en] Braid theory is a an important tool in low dimensional topology. In this work we study the braid group and see how it relates to knot theory. The main objective is to formulate and prove Alexander’s theorem stating that any knot, or more generally any link, can be obtained as the closure of a braid. We give two constructive proofs, one based on Alexander’s original proof and the other one following the Yamada–Vogel’s algorithm. Moreover, we provide the code of of an implementation of the latter algorithm, written in Python.