Braid Groups and their Representations

In this work we give a brief introduction to the braid groups. After giving different ways on how we could interpret these groups, we study some of the most famous linear representations: the Burau representation, and the Lawrence-Krammer-Bigelow representation. We will see whether these two are faithful or not. As a consequence we will show that these groups are linear, in other words that they can be embedded into a group of invertible matrices over some field.

In this work we give a brief introduction to the braid groups. After giving different ways on how we could interprete these groups, we study some of the most famous linear representations: the Burau representation, and the Lawrence-Krammer-Bigelow representation. We will see whether these two are faithful or not. As a consequence we will show that these groups are linear, in other words that they can be embedded into a group of invertible matrices over some field.