%0 Journal Article
%T Cohomology of the hyperelliptic Torelli group
%A Tara Brendle
%A Leah Childers
%A Dan Margalit
%J Mathematics
%D 2011
%I arXiv
%X Let SI(S_g) denote the hyperelliptic Torelli group of a closed surface S_g of genus g. This is the subgroup of the mapping class group of S_g consisting of elements that act trivially on H_1(S_g;Z) and that commute with some fixed hyperelliptic involution of S_g. We prove that the cohomological dimension of SI(S_g) is g-1 when g > 0. We also show that H_g-1(SI(S_g);Z) is infinitely generated when g > 1. In particular, SI(S_3) is not finitely presentable. Finally, we apply our main results to show that the kernel of the Burau representation of the braid group B_n at t = -1 has cohomological dimension equal to the integer part of n/2, and it has infinitely generated homology in this top dimension.
%U http://arxiv.org/abs/1110.0448v1