The Radul cocycle, the Chern–Connes character, and manifolds with conical singularities

Abstract

The present work is a continuation of a previous article of ours. First, we aim to explain how the residue index cocycle we had obtained, via pseudodifferential extensions, zeta functions and the boundary map in periodic cyclic cohomology, relates to the Connes–Moscovici residue cocycle. On the other hand, we explore the case of manifolds with conical singularities, and explain why J.-M. Lescure’s construction of a regular spectral triple in this situation cannot be significantly improved.