UBC Topology Seminar: Artem Kotelskiy (Online)

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 curve-invariants. Next, a criterion for when a bordered invariant can be viewed as an immersed curve will be given. Lastly, we will interpret knot Floer homology as an immersed curve in the twice-punctured disc, and describe how it is related to the immersed curve associated to the knot exterior. The talk is based on a joint work with Liam Watson and Claudius Zibrowius.