The \(K\)-theory localization of loops on an odd sphere and applications
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.
Snaith splitting of iterated loop spaces
scientific article; zbMATH DE number 488115
scientific article