A strong characterization of the entries of the Burau matrices of $4$-braids: The Burau representation of the braid group $B_4$ is faithful almost everywhere

Amitesh Datta

We establish strong constraints on the kernel of the (reduced) Burau representation ${\beta }_4:B_4\to {\text{GL}}_3\left(\mathbb{Z}\left[q^{\pm 1}\right]\right)$ of the braid group $B_4$.…