Waldhausen, Friedhelm Algebraic K-theory of spaces, concordance, and stable homotopy theory. (English) Zbl 0708.19001 Algebraic topology and algebraic K-theory, Proc. Conf., Princeton, NJ (USA), Ann. Math. Stud. 113, 392-417 (1987). [For the entire collection see Zbl 0694.00022.] Various splittings, up to homotopy, of the algebraic K-theory space A(X) of Waldhausen include \[ A(X)\simeq A^ S(X)\times Wh^{DIFF}(X)\text{ and } A^ S(X)\simeq \Omega^{\infty}S^{\infty}(X_+)\times \mu (X). \] The author uses a Kahn-Priddy type theorem to show \(\mu\) (x) is trivial, and therefore that \[ A(X)\simeq \Omega^{\infty}S^{\infty}(X_+)\times Wh^{DIFF}(X). \] He also discusses several other proofs of the vanishing of \(\mu\) (X). Reviewer: M.R.Stein Cited in 5 ReviewsCited in 14 Documents MSC: 19D10 Algebraic \(K\)-theory of spaces 55Q45 Stable homotopy of spheres Keywords:splittings of the algebraic K-theory space A(X) of Waldhausen; Kahn- Priddy theorem; homology; growth condition for homotopy groups Citations:Zbl 0694.00022 PDFBibTeX XML