Adam Levine 'Khovanov homology and cobordisms between split links'

Abstract: We discuss the (in)sensitivity of the Khovanov functor to four-dimensional linking of surfaces. We prove that if L and L' are split links, and C is a cobordism between L and L' that is the union of disjoint (but possibly linked) cobordisms between the components of L and the components of L', then the map on Khovanov homology induced by C is completely determined by the maps induced by the individual components of C and does not detect the linking between the components. As a corollary, we prove that a strongly homotopy-ribbon concordance (i.e., a concordance whose complement can be built with only 1- and 2-handles) induces an injection on Khovanov homology. This is joint work with Onkar Singh Gujral.