Algebraic & Geometric Topology

The link concordance invariant from Lee homology

John Pardon

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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 k2. 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
Received: 25 July 2011
Revised: 9 February 2012
Accepted: 14 February 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57Q60: Cobordism and concordance

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

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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