%0 Journal Article
%T Infinite generation of the kernels of the Magnus and Burau representations
%A Thomas Church
%A Benson Farb
%J Mathematics
%D 2009
%I arXiv
%R 10.2140/agt.2010.10.837
%X Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first homology. As a consequence we conclude that neither group has any finite generating set. The method of proof in each case consists of producing a kind of "Johnson-type" homomorphism to an infinite rank abelian group, and proving the image has infinite rank. For the case of Bur_n, we do this with the assistance of a computer calculation.
%U http://arxiv.org/abs/0909.4825v1