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Stable proofs of stable splittings

Published online by Cambridge University Press:  24 October 2008

Ralph L. Cohen
University of Chicago


V. P. Snaith's theorem giving splittings of the suspension spectrum of ΩnΣnX for a connected space X (8) has been exploited in several areas of homotopy theory. (See (2), (5) and (6), for instance.) Although this is a theorem about spectra, Snaith's proof (as well as a subsequent proof of Cohen, May, and Taylor (4)) proceeds unstably, on the space level. While the methods employed in these proofs are useful, they are somewhat complicated. The purpose of this note is to give a simple proof of this theorem, using only spectrum level arguments.

Research Article
Copyright © Cambridge Philosophical Society 1980

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