Matrix factorizations and higher residue pairings

TL;DR

This paper establishes a connection between the canonical pairing in periodic cyclic homology of matrix factorizations and the higher residue pairing on twisted de Rham cohomology for isolated singularities, bridging algebraic and geometric perspectives.

Contribution

It identifies the canonical pairing in the cyclic homology of matrix factorizations with the higher residue pairing, providing a new geometric interpretation.

Findings

Canonical pairing matches the higher residue pairing

Bridges algebraic and geometric approaches to singularities

Enhances understanding of matrix factorizations in singularity theory

Abstract

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 singularity the canonical pairing can be identified with the so-called higher residue pairing on the twisted de Rham cohomology of the singularity.