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 $1⟶P⟶B⟶W⟶1$. In this talk, I will explain how to determine the order of the extension $1⟶P/[P,P]⟶B/[P,P]⟶W⟶1$ 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.