The link concordance invariant from Lee homology

Abstract

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 {Pipe}L{Pipe}. The basic properties of the s -invariant all extend to the case of links; in particular, any orientable cobordism Σ between links induces a map between their corresponding vector spaces which is filtered of degree χ(Σ). A corollary of this construction is that any componentpreserving orientable cobordism from a Kh-thin link to a link split into k components must have genus at least ⌊k/2⌋. In particular, no quasi-alternating link is concordant to a split link.