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.
After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.