Geometry and Topology Seminar

We will discuss an approach to defining cobordism maps on link Floer homology. We will sketch the construction, and then describe some applications and interesting features. One application is a grading formula, which gives a bound on Upsilon for link cobordisms in negative definite 4--manifolds, generalizing some known bounds on Tau and Upsilon. We will sketch some other highlights and applications of the theory, including some formulas for mapping class group actions from moving basepoints, a formula for the conjugation action on connected sums of knots. As time permits we will describe some further connections between the link Floer TQFT and the Heegaard Floer invariants of closed 3- and 4-manifolds, such as graph TQFTs and adjunction inequalities.