Artem Kotelskiy

We will describe a geometric interpretation of Khovanov homology as Lagrangian Floer homology of two immersed curves in the 4-punctured 2-dimensional sphere. The main ingredient is a construction which translates Khovanov (or Bar-Natan) invariant of...

A variety of cut-and-paste techniques is being developed to study Khovanov, Heegaard Floer and instanton homologies. We will describe one of such techniques, centered around immersed curves in surfaces. First, we will give an overview of existing...