The contraderived category of linear factorizations and Khovanov-Rozansky knot homology

Abstract: In this talk I describe a notion of weak equivalence for linear factorizations (2-periodic complexes with d^2=0 replaced by d^2=w, originating from singularity theory) producing the homotopy category of matrix factorizations as the associated derived category. This is in analogy with the description of the homotopy category of projectives over a ring in terms of the derived category. The presence of the contraderived category sometimes simplifies the work with matrix factorizations; for example, it can be used to give an alternative construction of Khovanov-Rozansky's categorifications of the Quantum sl(k) knot invariants.