A large abelian quotient of the level 4 braid group

Geometry Topology Seminar
Monday, November 20, 2017 - 14:05
1 hour (actually 50 minutes)
Skiles 006
Georgia Institute of Technology
It is generally a difficult problem to compute the Betti numbers of a given finite-index subgroup of an infinite group, even if the Betti numbers of the ambient group are known. In this talk, I will describe a procedure for obtaining new lower bounds on the first Betti numbers of certain finite-index subgroups of the braid group. The focus will be on the level 4 braid group, which is the kernel of the mod 4 reduction of the integral Burau representation. This is joint work with Dan Margalit.