On a Hodge theoretic property of the Kuenneth map in periodic cyclic homology

TL;DR

This paper demonstrates that the K"unneth map in periodic cyclic homology respects a generalized Hodge filtration, linking algebraic structures with singularity theory through Thom-Sebastiani theorems.

Contribution

It establishes the compatibility of the K"unneth map with a generalized Hodge filtration in periodic cyclic homology, connecting algebraic and singularity theories.

Findings

K"unneth map is compatible with the generalized Hodge filtration

Connection established between cyclic homology and Thom-Sebastiani theorems

Provides new insights into the structure of periodic cyclic homology

Abstract

We prove that the standard K\"unneth map in periodic cyclic homology of differential Z/2-graded algebras is compatible with a generalization of the Hodge filtration and explain how this result is related to various Thom-Sebastiani type theorems in singularity theory.