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On the nonexistence of elements of Hopf invariant one. (English) Zbl 0178.26106
In this paper, the author outlines a proof of the extremely important result that there is bno element of Hopf invariant one in $$\pi_{2n-1}(S^n)$$ unless $$n = 2, 4$$, or $$8$$. The author gives the details of this proof in Ann. Math. (2) 72, 20–104 (1960; Zbl 0096.17404).
Reviewer: C. W. Patty

##### MSC:
 55Q25 Hopf invariants
topology
Full Text:
##### References:
 [1] José Adem, The iteration of the Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 720 – 726. · Zbl 0048.17002 [2] Henri Cartan, Sur l’itération des opérations de Steenrod, Comment. Math. Helv. 29 (1955), 40 – 58 (French). · Zbl 0064.17201 · doi:10.1007/BF02564270 · doi.org [3] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. · Zbl 0075.24305 [4] P. J. Hilton, An introduction to homotopy theory, Cambridge Tracts in Mathematics and Mathematical Physics, no. 43, Cambridge, at the University Press, 1953. · Zbl 0051.40302 [5] H. Hopf, Über die Abbildungen von Sphären auf Sphären niedriger Dimension, Fund. Math. vol. 25 (1935) pp. 427-440. · Zbl 0012.31902 [6] Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. · Zbl 0054.07103
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