Iterates of the suspension map and Mitchell's finite spectra with \(A_k\)-free cohomology
The author studies cross-effects of the unstable homotopy of spheres, which were previously constructed by \textit{M. Weiss} [Trans. Am. Math. Soc. 347, No. 10, 3743-3796 (1995; Zbl 0866.55020); erratum ibid. 359, No. 2, 851-855 (1998)]. He shows that \textit{S. A. Mitchell}'s finite spectra with \(A_k\)-free cohomology [Topology 24, 227-246 (1985; Zbl 0568.55021)] arise naturally as stabilization of these cross-effects. Moreover, he shows that (after suitable Bousfield localization) these cross-effects are homotopy equivalent to the infinite loop spaces associated with Mitchell's spectra.
scientific article; zbMATH DE number 1321862