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

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