Tuesday, May 2, 14:00, 7.527

Anne-Laure Thiel
Categorical action of the braid group of the cylinder.

Abstract:
In their seminal work, Khovanov and Seidel have used the polymorphous nature of the usual braid group (ie of finite type A) and hence its various definitions (diagrammatic presentation, mapping class group...) to construct a categorical action of this group which categorifies its famous Burau linear representation. The important fact is that this action detects subtle topological properties which ensures its faithfulness unlike the Burau linear representation. The aim of this talk is to describe a generalization of their approach to another Artin group, the one of type B - aka braid group of the cylinder or extended braid group of affine type A. Joint work with Agnès Gadbled and Emmanuel Wagner.