The link concordance invariant from Lee homology

John Pardon

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7 Scopus citations


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 {Pipe}L{Pipe}. 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 componentpreserving 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.

Original languageEnglish (US)
Pages (from-to)1081-1098
Number of pages18
JournalAlgebraic and Geometric Topology
Issue number2
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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