Braid groups are linear groups (Q1923996)

Let \(B_n\) denote the braid group on \(n\) strings. \(B_2\) is infinite cyclic and hence is a linear group. It is well-known that \(B_3\) is also a linear group. But it has remained an open problem as to whether any other braid groups are linear. In 1936 Burau gave a matrix representation of \(B_n\) and in 1961 Gassner generalized Burau's representation. The author shows that \(B_n\) is linear for all \(n\) by proving Theorem A. The Gassner representation of \(B_n\) is faithful for every \(n\).