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Limits of stable homotopy and cohomotopy groups

Published online by Cambridge University Press:  24 October 2008

J. D. S. Jones  and
S. A. Wegmann
J. D. S. Jones
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
S. A. Wegmann
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL
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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

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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
[2] Adams, J. F., Gunawardena, J. H. C. and Muller, H.. (To appear.)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] Steinberger, M.. Ph.D. thesis, University of Chicago, 1977.Google Scholar
[11] Wegmann, S. A.. P.hD. thesis, University of Warwick (in preparation).Google Scholar