Iterates of the suspension map and Mitchell's finite spectra with \(A_k\)-free cohomology
type: Item
instance of: scholarly article
title: Iterates of the suspension map and Mitchell's finite spectra with \(A_k\)-free cohomology
zbMATH Open document ID: 0930.55004
published in: Mathematical Research Letters
publication date: 2000-01-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 55P40
Mathematics Subject Classification ID: 55Q40
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55P65
zbMATH DE Number: 1321862
zbMATH Keywords: spheres
zbMATH Keywords: periodic homotopy
zbMATH Keywords: orthogonal calculus
author: Gregory Arone
reviewed by: Kohhei Yamaguchi
MaRDI profile type: Publication
DOI: 10.4310/MRL.1998.V5.N4.A6
description: scientific article; zbMATH DE number 1321862