Algebraic & Geometric Topology 12 (2012) 1081–1098

DOI: 10.2140/agt.2012.12.1081

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 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.

Keywords

Khovanov homology, link concordance, link cobordism, Rasmussen s-invariant, slice genus

Mathematical Subject Classification

Primary: 57M25, 57M27, 57Q60

References

Publication

Received: 25 July 2011
Revised: 9 February 2012
Accepted: 14 February 2012
Published: 7 May 2012

Authors