A large abelian quotient of the level 4 braid group

Geometry Topology Seminar
Monday, November 20, 2017 - 2:05pm
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.