THE BURAU REPRESENTATION OF THE BRAID GROUP Bn IS UNFAITHFUL FOR LARGE n

Two fundamental theorems of classical knot theory, by J. Alexander, are that every knot is a closed braid, and second, that a certain procedure (see [1,2] for both results) assigns to each knot K a polynomial A(K) in T, which only depends on the topological type of the knot once normalized by a power of T to take a positive value at T = 0. With this normalization, take T to be a transcendental number. Since 1926 [2], it has been known that the function A : Knots —• C is not one-to-one. However, it has not become clear whether the composite