Twisted Cyclic Cohomology and Modular Fredholm Modules

TL;DR

This paper extends the representation of cyclic cocycles as Chern characters to twisted cyclic cohomology using modular Fredholm modules, with examples from quantum groups and spheres.

Contribution

It introduces modular Fredholm modules for twisted cyclic cohomology, generalizing previous results and providing concrete examples from quantum geometry.

Findings

Representation of cyclic cocycles as Chern characters in twisted setting

Construction of modular Fredholm modules from Podleś spheres and SU_q(2)

Establishment of a new framework for twisted cyclic cohomology

Abstract

Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515-526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podle\'s spheres and from $SU_q(2)$.