Volume 7, issue 3 (2007)

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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 $s{l}_{3}$–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 $s{l}_{3}$–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 $s{l}_{2}$–link homology.

Keywords
$sl_3$, foams, Khovanov, link homology
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25, 81R50, 18G60
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