Tracing cyclic homology pairings under twisting of graded algebras

TL;DR

This paper explores how cyclic cohomology pairings behave under twisting of graded algebras, using monodromy and cup product actions to understand their structure.

Contribution

It provides a new description of cyclic cohomology and pairings with K-groups for 2-cocycle deformations of graded algebras, linking monodromy to group cohomology actions.

Findings

Describes cyclic cohomology for twisted graded algebras

Connects monodromy of Gauss-Manin connection to group cohomology

Provides tools for analyzing algebra deformations

Abstract

We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic cohomology in terms of the cup product action of group cohomology.