A presentation for the image of Burau(4) tensor Z_2

Daryl Cooper and D. Darren Long

The reduced Burau representation tensored with $Z_2$ of the $n$-string braid group $B_n$ maps $B_n\to GL(n-1,Z_2(t))$, and this determines an action of the $B_n$ on a Euclidean building. In the case $n=4$, we use this action to obtain a presentation of the iamge of the 4-string braid group.