Skip to main content Accessibility help
×
Home

Stable proofs of stable splittings

  • Ralph L. Cohen (a1)

Extract

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.

Copyright

References

Hide All
(1)Boardman, J. R. and Vogt, R. M.Homotopy invariant algebraic structures on topological spaces. Springer Lecture Notes in Mathematics, no. 347 (1973).
(2)Brown, E. H. Jr and Peterson, F. P.On the stable decomposition of Ω2S r + 2. Trans. Amer. Math. Soc. 243 (1978), 287298.
(3)Bruner, R., Lewis, G., May, J. P., McClure, J. and Steinberger, M.H ring spectra and their applications. Springer Lecture Notes in Mathematics. (To appear.)
(4)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of certain spaces CX. Math. Proc. Cambridge Philos. Soc. 84 (1978), 465496.
(5)Cohen, R. L. New infinite families in the stable homotopy groups of spheres and of Moore spaces. (To appear.)
(6)Mahowald, M.A new infinite family in . Topology 16 (1977), 249254.
(7)May, J. P.The geometry of iterated loop spaces. Springer Lecture Notes in Mathematics, no. 271 (1972).
(8)Snaith, V. P.A stable decomposition for ΩnSnX. J. London Math. Soc. 7 (1974), 577583.

Stable proofs of stable splittings

  • Ralph L. Cohen (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed