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

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.