How abelianization of subgroups of braid groups applies to cohomology
by Vincent Beck
Abstract: : 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 H2(W,P/[P,P]). The main ingredient is abelianization of subgroups of reflection groups and their braid groups.
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