The link concordance invariant from Lee homology

We use the knot homology of Khovanov and Lee to construct link concordance invariants generalizing the Rasmussen $s$-invariant of knots. The relevant invariant for a link is a filtration on a vector space of dimension $2^{\mathrm{\mid }L\mathrm{\mid }}$. The basic properties of the $s$-invariant all extend to the case of links; in particular, any orientable cobordism $\mathrm{\Sigma }$ between links induces a map between their corresponding vector spaces which is filtered of degree $\chi (\mathrm{\Sigma })$. A corollary of this construction is that any component preserving orientable cobordism from a $\text{Kh}$-thin link to a link split into $k$ components must have genus at least $\lfloor \frac{k}{2}\rfloor$. In particular, no quasi-alternating link is concordant to a split link.