## Algebraic & Geometric Topology

### The link concordance invariant from Lee homology

John Pardon

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 12, Number 2 (2012), 1081-1098.

Dates
Revised: 9 February 2012
Accepted: 14 February 2012
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715381

Digital Object Identifier
doi:10.2140/agt.2012.12.1081

Mathematical Reviews number (MathSciNet)
MR2928905

Zentralblatt MATH identifier
1263.57007

#### Citation

Pardon, John. The link concordance invariant from Lee homology. Algebr. Geom. Topol. 12 (2012), no. 2, 1081--1098. doi:10.2140/agt.2012.12.1081. https://projecteuclid.org/euclid.agt/1513715381

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