Abstract:Stable cohomotopy groups of Eilenberg-Mac Lane spectra of finite groups are shown to be trivial. This implies that the stable homotopy category, which is large enough to represent ordinary cohomology theory, cannot be self-dual. It can also be interpreted as an evidence to support Freyd’s generating hypothesis and a proof of a stable version of a conjecture of D. Sullivan.
- J. Frank Adams, Stable homotopy theory, Springer-Verlag, Berlin-Göttingen-Heidelberg-New York, 1964. Lectures delivered at the University of California at Berkeley, 1961; Notes by A. T. Vasquez. MR 0185597
- J. F. Adams and H. R. Margolis, Modules over the Steenrod algebra, Topology 10 (1971), 271–282. MR 294450, DOI 10.1016/0040-9383(71)90020-6 J. F. Adams, Stable homotopy and generalized homology, Mathematics Lecture Notes, Univ. of Chicago, 1971. J. Boardman, Stable homotopy theory, mimeograph notes, Univ. of Warwick, Coventry, England, 1965.
- J. M. Boardman, Stable homotopy theory is not self-dual, Proc. Amer. Math. Soc. 26 (1970), 369–370. MR 268887, DOI 10.1090/S0002-9939-1970-0268887-4
- B. Eckmann and P. J. Hilton, Exact couples in an abelian category, J. Algebra 3 (1966), 38–87. MR 191937, DOI 10.1016/0021-8693(66)90019-6
- Peter Freyd, Stable homotopy, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 121–172. MR 0211399
- Peter Hilton, Homotopy theory and duality, Gordon and Breach Science Publishers, New York-London-Paris, 1965. MR 0198466
- John C. Moore and Franklin P. Peterson, Nearly Frobenius algebras, Poincaré algebras and their modules, J. Pure Appl. Algebra 3 (1973), 83–93. MR 335572, DOI 10.1016/0022-4049(73)90007-8
- Goro Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan 25 (1973), 707–732. MR 341485, DOI 10.2969/jmsj/02540707
- N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 291-299
- MSC: Primary 55E10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402738-5
- MathSciNet review: 0402738