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H-spaces with generating subspaces*

Published online by Cambridge University Press:  14 November 2011

Norio Iwase
Norio Iwase
Affiliation:
Department of Mathematics, Kyushu University 33, Hakozaki Fukuoka 812, Japan
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Synopsis

For an H-space with a generating subspace, we construct a space whose K-cohomology is a direct sum of a truncated polynomial algebra and an ideal, which enables technical restrictions to be removed from several known results in the homotopy theory of H-spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 199 - 211
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Browder, W. and Thomas, E.. On the projective plane of an H-space. Illinois J. Math. 7 (1963), 492–502.CrossRefGoogle Scholar
2Hemmi, Y.. Certain 3-regular homotopy associative H-spaces (preprint).Google Scholar
3Hubbuck, J. R.. Hopf structures on Stiefel Manifolds. Math. Ann. 262 (1983), 529–547.CrossRefGoogle Scholar
4Hubbuck, J. R.. Products with the seven sphere and homotopy associativity. Mem. Fac. Sci. Kyushu Univ. Ser. A 40 (1986), 91–100.Google Scholar
5Hubbuck, J. R. and Mimura, M.. Certain p-regular H-spaces. Arch. Math. 49 (1987), 79–82.CrossRefGoogle Scholar
6Iwase, N.. On the ring structure of K*(XPn) (Master Thesis, Kyushu University, 1983 (in Japanese)).Google Scholar
7Iwase, N.. On the K-ring structure of X-projective n-space. Mem. Fac. Sci. Kyushu Univ. Ser. A 38 (1984), 285–297.Google Scholar
8Iwase, N. and Mimura, M.. Higher homotopy associativity. Arcata Proceedings (to appear).Google Scholar
9Iwase, N. and Mimura, M.. Higher homotopy associativity (in preparation).Google Scholar
10James, I. M.. The topology of Stiefel manifolds, London Math. Soc. Lecture Note Series 24 (Cambridge: Cambridge University Press, 1976).Google Scholar
11Kane, R.. Implications in Morava K-theory. Mem. Amer. Math. Soc. 59, No. 340 (1986).Google Scholar
12Lin, J. P.. Two torsion and loop space conjecture. Ann. of Math. 115 (1982), 35–91.CrossRefGoogle Scholar
13Sigrist, F. and Suter, U.. Sur l'associativité homotopique des H-espaces de range 2. C.R. Acad. Sci. Paris 273 (1971), 890–892.Google Scholar
14Sigrist, F. and Suter, U.. Eine Anwendung der K-Theorie in der H-Räume. Comment. Math. Helv. 47 (1972), 36–52.CrossRefGoogle Scholar
15Stasheff, J. D.. Homotopy associativity of H-spaces, I and II. Trans. Amer. Math. Soc. 108 (1963), 275–292 and 293–312.Google Scholar
16Thomas, E.. On functional cup products and the transgression operator. Arch. Math. 12 (1961), 435–444.CrossRefGoogle Scholar
17Thomas, E.. On the mod 2 cohomology of certain H-spaces. Comment. Math. Helv. 37 (1962), 130–140.CrossRefGoogle Scholar
18Thomas, E.. Steenrod squares and H-spaces II. Ann. of Math. 81 (1965), 483–495.CrossRefGoogle Scholar
19Zabrodsky, A.. On spherical classes in the cohomology of H-spaces. H-spaces Neuchatel (Suisse) Août 1970, Lecture Notes in Mathematics 196, 25–33 (Berlin: Springer, 1971).Google Scholar