On the Burau representation of B_{4} 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 A^{3} and B^{3} generate a free
group of rank two [Mor], [WitZar], [BerTra_{1}]. We prove that
they also generate a free group when considered as matrices
over the Z^{p}[t,t^{1}] for any integer p > 1.
Tbilisi Mathematical Journal, Special Issue (7  2021), pp. 5762
