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 $2^{|L|}$. 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 $\chi (\Sigma )$. 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 $\lfloor \frac{k}{2}\rfloor$. In particular, no quasi-alternating link is concordant to a split link.

15 pages, 1 figure

References in corpus (3)

• On the Khovanov and knot Floer homologies of quasi-alternating links
• Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
• Khovanov's invariant for closed surfaces

Cited by in corpus (9)

• The concordance invariant tau in link grid homology
• The rational Khovanov homology of 3-strand pretzel links
• On the slice genus and some concordance invariants of links
• Lee filtration structure of torus links
• Monoids in the mapping class group
• On the Kronheimer-Mrowka concordance invariant
• A Remark on the Lewark-Zibrowius Invariant
• Cobordisms to weakly splittable links
• Comparing Bennequin-type inequalities