38 citations · 77 across the 7 of their papers we have counts for
9 papers
On Hochschild invariants of Landau-Ginzburg orbifolds
Dmytro Shklyarov
We develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetr…
Calabi-Yau structures on categories of matrix factorizations
Dmytro Shklyarov
We write out explicit proper Calabi-Yau structures, i. e. non-degenerate cyclic cocycles on the differential graded categories of matrix factorizations of regular functions with is…
Exponentially twisted cyclic homology
Dmytro Shklyarov
By a theorem of Bernhard Keller the de Rham cohomology of a smooth variety is isomorphic to the periodic cyclic homology of the differential graded category of perfect complexes on…
Matrix factorizations and higher residue pairings
Dmytro Shklyarov
The periodic cyclic homology of any proper dg category comes equipped with a canonical pairing. We show that in the case of the dg category of matrix factorizations of an isolated…
On a Hodge theoretic property of the Kuenneth map in periodic cyclic homology
Dmytro Shklyarov
We prove that the standard Künneth map in periodic cyclic homology of differential Z/2-graded algebras is compatible with a generalization of the Hodge filtration and explain how t…
Non-commutative Hodge structures: Towards matching categorical and geometric examples
D. Shklyarov
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss e…