## University of Sydney Algebra Seminar

# Vincent Beck (ENS Cachan)

## Friday 15 April, 12:05-12:55pm, Carslaw 175

### Abelianization in braid group

Let \(W\) be a complex reflection group. It is easy to define the braid group B and the pure braid group P associated to W, which are related by the exact sequence \(1 \longrightarrow P \longrightarrow B \longrightarrow W \longrightarrow 1\). In this talk, I will explain how to determine the order of the extension \(1\longrightarrow P/[P,P]\longrightarrow B/[P,P] \longrightarrow W \longrightarrow 1\) viewed as an element of the second cohomology group \(H^2(W,P/[P,P])\). The main ingredient is abelianization of subgroups of reflection groups and their braid groups.