Abstract
We determine the coalgebra structure for K(1)*Ωk S 2n+1 and thus complete the description as Hopf algebras. We also study the higher order K-theory Bockstein structure for K(1)*(Ωk S 2n+1). To do this we use the p-local K-theory equivalences given by Bousfield and the author in [1] and [4]. We then may use the results of McClure. who determines the K-theory Bockstein spectral sequence for Ω∞Σ∞ X. As an application we use the existence of elements of order p r in K-theory to determine a lower bound for the suspension order of the stable summands of Ω2k S 2n+1. Using the upper bound results of Silberbush this gives the suspension order at odd primes.
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© 1996 Birkhäuser Verlag
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Langsetmo, L. (1996). Further Structure in K(1)*Ωk S 2n+1 . In: Broto, C., Casacuberta, C., Mislin, G. (eds) Algebraic Topology: New Trends in Localization and Periodicity. Progress in Mathematics, vol 136. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9018-2_17
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DOI: https://doi.org/10.1007/978-3-0348-9018-2_17
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