A PRESENTATION FOR THE IMAGE OF BURAU(4) ⊗ Z_{2}

Daryl Cooper D. Darren Long

Abstract. The reduced Burau representation tensored with Z_{2} of the n-string braid group B_{n} maps B_{n} → 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.

Typeset by AMS-TEX