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Relations in stable homotopy modules


Author: Donald W. Kahn
Journal: Proc. Amer. Math. Soc. 40 (1973), 253-259
MSC: Primary 55E45
DOI: https://doi.org/10.1090/S0002-9939-1973-0436139-8
MathSciNet review: 0436139
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Abstract: The ``generating hypothesis'' of Freyd implies various fascinating statements in stable homotopy, particularly about the stable homotopy ring of spheres and the modules over this ring. The present paper extends some of these consequences. It also investigates the question of whether a possible counterexample to the hypothesis might be detected by its action on homology groups; for this, we find a connection with work of Joel Cohen on coherent graded rings.


References [Enhancements On Off] (What's this?)

  • [1] Joel Cohen, Coherent graded rings and the non-existence of spaces of finite stable homotopy-type, Comment, Math. Helv. 44 (1969), 217-228. MR 40 #892. MR 0247628 (40:892)
  • [2] P. Freyd, Stable homotopy, Proc. Conference on Categorical Algebra (La Jolla, Calif., 1965), Springer-Verlag, New York, 1966, pp. 121-172. MR 35 #2280. MR 0211399 (35:2280)
  • [3] Donald W. Kahn, Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432-450. MR 27 #764. MR 0150777 (27:764)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0436139-8
Keywords: Stable homotopy modules, generating hypothesis
Article copyright: © Copyright 1973 American Mathematical Society

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