Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras

TL;DR

This paper provides a new quantitative approach to understanding the cyclic cohomology of biflat Banach algebras, showing they have the same cyclic cohomology as the complex numbers, without using the Connes-Tsygan sequence.

Contribution

It introduces a quantitative variant of the classical result on biflat Banach algebras' cyclic cohomology, avoiding reliance on the Connes-Tsygan exact sequence.

Findings

Biflat Banach algebras have cyclic cohomology equal to that of a5

A new quantitative method for analyzing cyclic cohomology is developed

The approach is inspired by classical constructions but does not depend on the exact sequence

Abstract

We revisit the old result that biflat Banach algebras have the same cyclic cohomology as $\mathbb C$, and obtain a quantitative variant (which is needed in forthcoming joint work of the author). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [Connes,1985] and [Helemskii,1992].