The universal $sl_3$–link homology

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.