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The link concordance invariant from Lee homology

John Pardon

Algebraic & Geometric Topology 12 (2012) 1081–1098

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 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 component-preserving orientable cobordism from a Kh–thin link to a link split into k components must have genus at least k2. In particular, no quasi-alternating link is concordant to a split link.

Khovanov homology, link concordance, link cobordism, Rasmussen s-invariant, slice genus
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57Q60
Received: 25 July 2011
Revised: 9 February 2012
Accepted: 14 February 2012
Published: 7 May 2012
John Pardon
Department of Mathematics
Stanford University
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Stanford CA 94305