On transfer maps in the algebraic $K$-theory of spaces

Abstract

We show that the Waldhausen trace map ${\mathrm{Tr}}_X:A(X)\to Q{X}_{+}$, which defines a natural splitting map from the algebraic $K$-theory of spaces to stable homotopy, is natural up to \emph{weak} homotopy with respect to transfer maps in algebraic $K$-theory and Becker-Gottlieb transfer maps respectively.

arXiv comment16 pages. Final version; to appear in Math. Z