The link concordance invariant from Lee homology

Pardon, John¹

¹Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford CA 94305, USA

Algebraic and Geometric Topology, Tome 12 (2012) no. 2, pp. 1081-1098

Résumé

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 ⌊k∕2⌋. In particular, no quasi-alternating link is concordant to a split link.

Détail

DOI : 10.2140/agt.2012.12.1081

Classification : 57M25, 57M27, 57Q60
Keywords: Khovanov homology, link concordance, link cobordism, Rasmussen s-invariant, slice genus

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