Limits of stable homotopy and cohomotopy groups
Published online by Cambridge University Press: 24 October 2008
Extract
In this paper we formulate and prove generalizations of a theorem of Lin [7]. Let X be a CW complex with base point x0. Define a free involution T on S∞×(X Λ X) by T (w, xΛy) = (−w, yΛx). The quadratic construction on X is the complex
This construction can be applied to spectra. A complete and thorough account will appear in the work on equivariant stable homotopy theory in preparation by L. G. Lewis, J. P. May, J. McLure and M. Steinberger. Some of the results are announced in [8].
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 473 - 482
- Copyright
- Copyright © Cambridge Philosophical Society 1983
References
[1] Adams, J. F.. Graeme Segal's Burnside ring conjecture. Topology Symposium, Siegen 1979. Lecture Notes in Math. vol. 788 (Springer-Verlag, 1980).Google Scholar
[3] Carlsson, G.. Equivariant stable homotopy and Segal's conjecture. (To appear.)Google Scholar
[4] Gray, B.. Homotopy Theory: An Introduction to Algebraic Topology (Academic Press, 1975).Google Scholar
[5] Gunawardena, J. H. C.. Segal's conjecture for cyclic groups of (odd) prime order. J. T. Knight Prize Essay, Cambridge 1980.Google Scholar
[6] Jones, J. D. S.. The Kervaire invariant of extended power manifolds. Topology 17 (1978), 249–286.Google Scholar
[7] Lin, W. H.. On conjectures of Mahowald, Segal and Sullivan. Math. Proc. Cambridge Philos. Soc. 87 (1980), 449–458.Google Scholar
[8] May, J. P., H∞ ring spectra and their applications. Proc. Symp. Pure Math. vol. XXXII, part 2. A.M.S. (1978), 229–243.Google Scholar
[9] Singer, W. M.. A new chain complex for the homology of the Steenrod algebra. Math. Proc. Cambridge Philos. Soc. 90 (1981), 279–293.CrossRefGoogle Scholar
- 10
- Cited by