Image of the Burau Representation at $d$-th Roots of unity

Abstract

We prove that the image of the Full braid group $B_{n+1}$ on $n+1$ strands under the Burau representation, evaluated at a primitive $d$-th root of unity is arithmetic provided $n\geq d$.Comment: To appear in Annals of Mathematics. arXiv admin note: text overlap with arXiv:1204.477