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Homotopy groups and H-maps

Published online by Cambridge University Press:  20 January 2009

Alain Jeanneret
Alain Jeanneret
Affiliation:
Universität Bern, Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern
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Abstract

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The first nonvanishing homotopy group of a finite H-space X whose mod 2 homology ring is associative occurs in degrees 1, 3 or 7. Generators of these groups can be represented by maps α:Sn→X for n = 1, 3 or 7. In this note we prove that under some hypothesis on X there exists an H-structure on Sn, n = 1, 3 or 7 such that α is an H-map.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 465 - 473
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Adams, J. F., Vector fields on spheres, Ann. of Math. 75 (1962), 603–632.CrossRefGoogle Scholar
2.Browder, W. and Thomas, E., On the projective plane of an H-space, Illinois J. Math. 7 (1963), 492–502.CrossRefGoogle Scholar
3.Dwyer, W. G. and Wilkerson, C. W., A new finite loop space at the prime two, J. Amer. Math.Soc. 6 (1993), 37–64.CrossRefGoogle Scholar
4.Goncalves, D. L., Mod 2 homotopy associative H-spaces (Lecture Notes in Mathematics, 657, 1978), 198–216.CrossRefGoogle Scholar
5.Hilton, P., Homotopy theory and duality (Gordon and Breach, 1965).Google Scholar
6.James, I. M., Multiplications on spheres III, Trans. Amer. Math. Soc. 84 (1957), 545–558.Google Scholar
7.Jeanneret, A. et Lin, J. P., Connexité des H-spaces finis, C. R. Acad. Sci. Pari. 315 (1992), 829–831.Google Scholar
8.Kane, R. M., Implications in Morava K-theory, Mem. Amer. Math. Soc. 340 (1986).Google Scholar
9.Lin, J. P., Torsion in H-spaces II, Ann. of Math. 107 (1978), 41–88.CrossRefGoogle Scholar
10.Lin, J. P., 4k+ 1 dimensional generators of finite H-spaces, manuscript.Google Scholar
11.Mahamed, N., Piccinini, R. and Suter, U., Some Applications of Topological K-Theory (North-Holland Mathematics Studies 45, 1980).Google Scholar
12.Mimura, M. and Toda, H., Topology of Lie groups I and II (Amer. Math. Soc. Translations of Mathematical Monographs, 1991).Google Scholar
13.Schiffman, S. J., A Samelson product and homotopy associativity, Proc. Amer. Math. Soc. 70 (1978), 189–195.CrossRefGoogle Scholar