The Burau representation is not faithful for n ≥ 6

This should be contrasted with the method of [6] which in this context involves a passage from n to n + 2. In fact our methods produce examples which are substantially simpler than those constructed in [6] at least measured by crossing number. This obstruction can also be used to give elements in the kernel of the representation obtained from the Burau reprcscntation of the five strand braid group by reducing all coefficients modulo 2. Some extra ideas arc required in order to keep some of the linear algebra under control and we need to appeal to the following result regarding Burau matrices: