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H-Equivalence Classes of Multiplications on Certain Fiber Spaces

Published online by Cambridge University Press:  20 November 2018

Chao-Kun Cheng
Chao-Kun Cheng*
Affiliation:
State University College, Potsdam, New York
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The enumeration of the H-equivalence classes of multiplications on a space is a topic of current interest. In this paper we try to study the H-equivalence classes of multiplications on a CW complex X with finitely many non-vanishing homotopy groups, by using the Postnikov decomposition of X and multiplier arguments [1; 4], This paper presents a way to compute the set of H-equivalence classes of multiplications on X from the knowledge of certain quotient sets of H*(B Λ B, ∑) and some homotopy equivalences of B, where B represents the spaces in the Postnikov decomposition of X, and ∑ denotes abelian groups corresponding to the homotopy groups of X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 752 - 765
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Cheng, C. K., Multiplications on a space with finitely many non-vanishing homotopy groups, Can. J. Math. 24 (1972), 1052–1062.Google Scholar
2. James, I. M., On H-spaces and their homotopy groups, Quart. J. Math. Oxford Ser. 11 (1960), 161–179.Google Scholar
3. Kahn, D. W., Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432–450.Google Scholar
4. Stasheff, J. D., On extensions of Espaces, Trans. Amer. Math. Soc. 105 (1962), 126–135.Google Scholar
5. Stasheff, J. D., H-space problems, H-spaces, Neuchâtel (Suisse), Août 1970 (Springer-Verlag Notes, Vol. 196) 122–136.Google Scholar
6. Williams, F. D., Quasi-commutativity of H-spaces, Michigan Math. J. 19 (1972), 209–213.Google Scholar