# 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.