#### Volume 8, issue 1 (2008)

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The foam and the matrix factorization $\mathit{sl}_3$ link homologies are equivalent

### Marco Mackaay and Pedro Vaz

Algebraic & Geometric Topology 8 (2008) 309–342
##### Abstract

We prove that the universal rational ${sl}_{3}$ link homologies which were constructed by Khovanov in [?] and the authors in [?], using foams, and by Khovanov and Rozansky in [?], using matrix factorizations, are naturally isomorphic as projective functors from the category of links and link cobordisms to the category of bigraded vector spaces.

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