The universal sl3–link homology

Mackaay, Marco; Vaz, Pedro

doi:10.2140/agt.2007.7.1135

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The universal $sl_3$–link homology

Marco Mackaay and Pedro Vaz

Algebraic & Geometric Topology 7 (2007) 1135–1169

DOI: 10.2140/agt.2007.7.1135

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

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

Volume 7, issue 3 (2007)