Matrix factorizations via Koszul duality

Abstract

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.

Latex 34 pages, rewritten introduction, deleted an appendix, minor modification on proofs, final version

References in corpus (3)

• On the perturbation lemma, and deformations
• Orlov spectra: bounds and gaps
• Curved A-infinity algebras and Landau-Ginzburg models

Cited by in corpus (9)

• Hochschild (co)homology of the second kind I
• Curved A-infinity algebras and Landau-Ginzburg models
• Noncommutative homological mirror functor
• A category of kernels for equivariant factorizations and its implications for Hodge theory
• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
• Hybrid models for homological projective duals and noncommutative resolutions
• G-twisted braces and orbifold Landau-Ginzburg Models
• Homological perturbation theory with curvature
• Kodaira-Spencer map, Lagrangian Floer theory and orbifold Jacobian algebras