The \(K\)-theory localization of loops on an odd sphere and applications
type: Item
instance of: scholarly article
title: The \(K\)-theory localization of loops on an odd sphere and applications
zbMATH Open document ID: 0808.55003
DOI: 10.1016/0040-9383(93)90009-K
author: Lisa Langsetmo
published in: Topology
publication date: 1995-03-16T00:00:00Z
review text: The author constructs the K-theory localization of \(\Omega S^{2n + 1}\) and \(\Omega^ 2 S^{2n + 1}\). That is, maps are constructed from these spaces into K-local spaces which induce isomorphisms in (complex periodic) K-theory. In [\textit{M. Mahowald} and \textit{R. Thompson}, ibid. 31, No. 1, 133-141 (1992; Zbl 0759.55010)] the K-theory localization of \(S^{2n + 1}\) was constructed using maps coming from the reviewer's stable decomposition of the iterated loop spaces, \(\Omega^ m \Sigma^ m S^{2n + 1}\). K-theory localization does not automatically respect taking loops so, while the author's result uses the same maps in its construction, it must be derived independently.
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 488115
zbMATH Keywords: Snaith splitting of iterated loop spaces
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: 0040-9383(93)90009-k
OpenAlex ID: W2087172077
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description: scientific article; zbMATH DE number 488115