Geometry and Topology Seminar

In 1994, Bass and Lubotzky introduced the notion of a "linear-central filtration" which is a structure present in many situations in geometric group theory, e.g. in the Johnson filtration of the mapping class group of a surface. We survey here some recent work investigating the Burau representation of the braid group using these tools. Our main result is a complete and simple description of the image of the Burau representation, answering a 1974 question of Birman. We are also able to obtain a new abelian quotient of the so-called braid Torelli group. Portions of this work are joint with Kevin Kordek.