Tuesday, May 2, 14:00, 7.527
Categorical action of the braid group of the cylinder.
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.