Relative Khovanov-Jacobsson classes for spanning surfaces

Abstract

We define the Khovanov-Jacobsson class for a properly embedded surface in the 4-ball, an element of the Khovanov homology of its boundary link in the 3-sphere. We then develop general non-triviality criteria for Khovanov homology classes, and use these to distinguish the Khovanov-Jacobsson classes of various families of surfaces. Among these are pairs of distinct slice disks for pretzel knots, and the first known examples of pairs of Seifert surfaces of equal genus for links in the 3-sphere that remain distinct when pushed into the 4-ball.