On the Burau representation of B4 modulo p

A. Beridze, S. Bigelow, P. Traczyk

The problem of faithfulness of the (reduced) Burau representation for n =4 is known to be equivalent to the problem of whether certain two matrices A and B generate a free group of rank two. It is known that A3 and B3 generate a free group of rank two [Mor], [Wit-Zar], [Ber-Tra1]. We prove that they also generate a free group when considered as matrices over the Zp[t,t-1] for any integer p > 1. 

Tbilisi Mathematical Journal, Special Issue (7 - 2021), pp. 57-62