30 research outputs found
Matrix factorizations via Koszul duality
In this paper we prove a version of curved Koszul duality for Z/2Z-graded
curved coalgebras and their coBar differential graded algebras. A curved
version of the homological perturbation lemma is also obtained as a useful
technical tool for studying curved (co)algebras and precomplexes.
The results of Koszul duality can be applied to study the category of matrix
factorizations MF(R,W). We show how Dyckerhoff's generating results fit into
the framework of curved Koszul duality theory. This enables us to clarify the
relationship between the Borel-Moore Hochschild homology of curved (co)algebras
and the ordinary Hochschild homology of the category MF(R,W). Similar results
are also obtained in the orbifold case and in the graded case.Comment: Latex 34 pages, rewritten introduction, deleted an appendix, minor
modification on proofs, final versio