Geometri och topologi: Categorical action of the braid group of the cylinder: symplectic aspect
- Plats: Ångströmlaboratoriet
- Föreläsare: Agnès Gadbled (Uppsala)
- Kontaktperson: Maksim Maydanskiy
Abstract : Khovanov and Seidel gave in 2000 an action of the classical braid group on a category of algebraic nature that categorifies the Burau representation. They proved the faithfulness of this action through the study of curves in a punctured disk (while Burau representation is not faithful for braids with five strands or more). In a recent article with Anne-Laure Thiel and Emmanuel Wagner, we extended this result to the braid group of the cylinder.
The work of Khovanov and Seidel also had a symplectic aspect that we now generalize. In this talk, I will explain the strategy and tools to get a symplectic monodromy in our case and prove its injectivity. If time permits, I will explain how this action lifts to a symplectic categorical representation on a Fukaya category that should be related to the algebraic categorical representation.
This is a joint work in progress with Anne-Laure Thiel and Emmanuel Wagner