On the functoriality of Khovanov–Floer theories

Abstract

We introduce the notion of a Khovanov–Floer theory. We prove that every page (after E1) of the spectral sequence accompanying a Khovanov–Floer theory is a link invariant, and that an oriented link cobordism induces a map on each page which is an invariant of the cobordism up to smooth isotopy rel boundary. We then prove that the spectral sequences relating Khovanov homology to Heegaard Floer homology and singular instanton knot homology are induced by Khovanov–Floer theories and are therefore functorial in the manner described above, as had been conjectured for some time.