Khovanov homology and knot Floer homology for pointed links.

A well-known conjecture states that for any -component link in , the rank of the knot Floer homology of (over any field) is less than or equal to times the rank of the reduced Khovanov homology of . In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field . [ABSTRACT FROM AUTHOR]