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

TL;DR

This paper explores the connection between the Radul cocycle and the Connes-Moscovici residue cocycle, focusing on manifolds with conical singularities where complex zeta functions pose analytical challenges.

Contribution

It establishes a relationship between two residue cocycles and discusses their application to singular manifolds with complex spectral properties.

Findings

Linked Radul and Connes-Moscovici cocycles in singular settings

Analyzed zeta functions with higher-order poles on conical manifolds

Provided insights into noncommutative geometric invariants for singular spaces

Abstract

This short note establishes a relationship between a generalized version of the Radul residue cocycle introduced in former works of the author and the Connes-Moscovici residue cocycle, and discusses the applicability of such a formula to manifolds with conical singularities, where zeta functions of Fuchs-type pseudodifferential operators may exhibit double or triple poles.