El grup de trenes i espais de configuracions

Abstract

[en] Braid theory was first formally introduced by Emil Artin in the 1920s as a way to study the topology of knots. Since then, braid groups have been the subject of extensive research, leading to a wealth of results and applications. The main objective of this work is to understand what braids are in their entirety, first giving a geometric description of them and then an algebraic one. These two descriptions allow us to relate braids to other branches of mathematics that, a priori, may seem unrelated. With this, we introduce the existing connection between configuration spaces and braid group, which will allow us to demonstrate that any braid, as an element of a group, has infinite order. Finally we give another view of braids by relating them to the mapping class groups.