The link concordance invariant from Lee homology

Details The link concordance invariant from Lee homology The link concordance invariant from Lee homology

2011-07-23

arxiv.org/abs/1107.4702v2

Mathematics

Geometric Topology

15 pages, 1 figure

Scientific paper

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 $\lfloor\frac k2\rfloor$. In particular, no quasi-alternating link is concordant to a split link.

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