Volume 7, issue 3 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The universal $sl_3$–link homology

Marco Mackaay and Pedro Vaz

Algebraic & Geometric Topology 7 (2007) 1135–1169

arXiv: math.GT/0603307

Abstract

We define the universal sl3–link homology, which depends on 3 parameters, following Khovanov’s approach with foams. We show that this 3–parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov’s original sl3–link homology belongs, the second is the one studied by Gornik in the context of matrix factorizations and the last one is new. Following an approach similar to Gornik’s we show that this new link homology can be described in terms of Khovanov’s original sl2–link homology.

Keywords
$sl_3$, foams, Khovanov, link homology
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25, 81R50, 18G60
References
Publication
Received: 8 May 2007
Accepted: 30 May 2007
Published: 9 August 2007
Authors
Marco Mackaay
Departamento de Matemática
Universidade do Algarve
Campus de Gambelas
8005-139 Faro
Portugal
Pedro Vaz
Departamento de Matemática
Universidade do Algarve
Campus de Gambelas
8005-139 Faro
Portugal