Non-commutative Hodge structures: Towards matching categorical and geometric examples

Shklyarov, D.

doi:10.1090/S0002-9947-2014-05913-8

Non-commutative Hodge structures: Towards matching categorical and geometric examples
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Trans. Amer. Math. Soc. 366 (2014), 2923-2974 Request permission

Abstract:

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 explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce, up to a certain shift, a well-known connection on the associated twisted de Rham cohomology which plays a central role in the geometric approach to the Hodge theory of isolated singularities.

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