Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T17:08:07.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Commutative products on spheres

Published online by Cambridge University Press:  24 October 2008

I. M. James
I. M. James
Affiliation:
The Institute for Advanced StudyPrinceton, New Jersey
Get access Rights & Permissions [Opens in a new window]

Extract

Consider a topological n–sphere Sn, where n ≥ 1. By a commutative product I mean a continuous function f: Sn × Sn → Sn such that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 63 - 68
Copyright
Copyright © Cambridge Philosophical Society 1957

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Barratt, M. G.Homotopy ringoids and homotopy groups. Quart. J. Math. Oxford (2), 5 (1954), 271–90.CrossRefGoogle Scholar
(2)Eilenberg, S.Cohomology and continuous mappings. Ann. Math., Princeton, 41 (1940), 231–51.CrossRefGoogle Scholar
(3)Eilenberg, S. and Maclane, S.On the groups H(II, n). II. Ann. Math., Princeton, 60 (1954), 49–139.CrossRefGoogle Scholar
(4)Helton, P. J.The Hopf invariant and homotopy groups of spheres. Proc. Camb. Phil. Soc. 48 (1952), 547–54.CrossRefGoogle Scholar
(5)Hopf, H.Über die Abbildungen von Sphären auf Sphären niedrigerer Dimension. Fundam. Math. 25 (1935), 427–440.CrossRefGoogle Scholar
(6)Liao, S. D.On the topology of the cyclic products of spheres. Trans. Amer. Math. Soc. 77 (1954), 520–51.CrossRefGoogle Scholar
(7)Nakaoka, M.Homotopy of the two-fold symmetric products of spheres. J. Inst. Polyt., Osaka, 6 (1955), 19–30.Google Scholar
(8)Serre, J.-P.Homologie singulière des espaces fibrés. Ann. Math., Princeton, 54 (1951), 425–505.CrossRefGoogle Scholar
(9)Serre, J.-P.Groupes d'homotopie et classes de groupes abéliens. Ann. Math., Princeton, 58 (1953), 258–94.CrossRefGoogle Scholar
(10)Toda, H.Generalized Whitehead products and homotopy groups of spheres. J. Inst. Polyt., Osaka, 3 (1952), 43–82.Google Scholar
(11)Whitehead, G. W.A generalization of the Hopf invariant. Ann. Math., Princeton, 51 (1950), 192–237.CrossRefGoogle Scholar
(12)Whitehead, J. H. C.On the theory of obstructions. Ann. Math., Princeton, 54 (1951), 68–84.CrossRefGoogle Scholar