The First Differential of the Functor "Algebraic K-Theory of Spaces"

Abstract

In his "Algebraic K-theory of topological spaces II" Waldhausen proved that his functor A(X) splits: There is a canonical map from the stable homotopy of X which has a retraction up to weak equivalence. We adapt Waldhausen's proof to obtain a calculation of the Differential (in the sense of Goodwillie's "Calculus I") of A(X) at any path-connected base space.Comment: The calculation of the differential in Section 7 contains a mistake and it is not clear if the statement hold