Quasihomomorphisms and the residue Chern character

TL;DR

This paper introduces a new method using renormalized eta-cochains to find local representatives of the bivariant Chern character for finitely summable quasihomomorphisms, connecting to quantum field theory anomalies.

Contribution

It provides a general procedure for localizing the bivariant Chern character and generalizes the Connes-Moscovici residue formula through zeta-function renormalization.

Findings

Derived local representatives of the bivariant Chern character.

Established a bivariant generalization of the residue formula.

Linked the mathematical framework to quantum field theory anomalies.

Abstract

We develop a general procedure, based on the renormalized eta-cochain, which allows to find local representatives of the bivariant Chern character of finitely summable quasihomomorphisms. In particular, using zeta-function renormalization we obtain a bivariant generalization of the Connes-Moscovici residue formula, and explain the link with chiral and multiplicative anomalies in quantum field theory.