On the kernel of the Gassner representation

Abstract

We study the Gassner representation of the pure braid group $P_n$ by considering its restriction to a free subgroup $F$. The kernel of the restriction is shown to lie in the subgroup $[{\Gamma }^{3}F,{\Gamma }^{2}F]$, sharpening a result of Lipschutz.

9 pages, final version to appear in Arch. Math. (Basel)