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2012 The link concordance invariant from Lee homology
John Pardon
Algebr. Geom. Topol. 12(2): 1081-1098 (2012). DOI: 10.2140/agt.2012.12.1081


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 k2. In particular, no quasi-alternating link is concordant to a split link.


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John Pardon. "The link concordance invariant from Lee homology." Algebr. Geom. Topol. 12 (2) 1081 - 1098, 2012.


Received: 25 July 2011; Revised: 9 February 2012; Accepted: 14 February 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1263.57007
MathSciNet: MR2928905
Digital Object Identifier: 10.2140/agt.2012.12.1081

Primary: 57M25 , 57M27 , 57Q60

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

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2012
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