Relations in stable homotopy modules
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- by Donald W. Kahn PDF
- Proc. Amer. Math. Soc. 40 (1973), 253-259 Request permission
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
- Joel M. Cohen, Coherent graded rings and the non-existence of spaces of finite stable homotopy type, Comment. Math. Helv. 44 (1969), 217–228. MR 247628, DOI 10.1007/BF02564524
- Peter Freyd, Stable homotopy, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 121–172. MR 0211399
- Donald W. Kahn, Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432–450. MR 150777, DOI 10.1090/S0002-9947-1963-0150777-X
- Donald W. Kahn, A note on stable homotopy modules, Proc. Amer. Math. Soc. 26 (1970), 683–686. MR 270368, DOI 10.1090/S0002-9939-1970-0270368-9
- Donald W. Kahn, Stable spectral sequences and their applications, Amer. J. Math. 94 (1972), 1131–1154. MR 310876, DOI 10.2307/2373567
Additional Information
- © Copyright 1973 American Mathematical Society
- 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