#### Volume 12, issue 2 (2012)

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The link concordance invariant from Lee homology

### John Pardon

Algebraic & Geometric Topology 12 (2012) 1081–1098
##### 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 ${2}^{|L|}$. The basic properties of the $s$–invariant all extend to the case of links; in particular, any orientable cobordism $\Sigma$ between links induces a map between their corresponding vector spaces which is filtered of degree $\chi \left(\Sigma \right)$. A corollary of this construction is that any component-preserving 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.