Twisted Cyclic Cohomology and Modular Fredholm Modules

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 Podleś spheres and from $S{U}_q(2)$.

References in corpus (6)

• Type III and spectral triples
• Index theory for locally compact noncommutative geometries
• A twisted spectral triple for quantum SU(2)
• A residue formula for the fundamental Hochschild 3-cocycle for SUq(2)
• On the noncommutative spin geometry of the standard Podles sphere and index computations
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podles sphere

Cited by in corpus (1)

• On modular semifinite index theory