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H-Equivalence Classes of Multiplications on Certain Fiber Spaces

  • Chao-Kun Cheng (a1)

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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.

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References

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1. Cheng, C. K., Multiplications on a space with finitely many non-vanishing homotopy groups, Can. J. Math. 24 (1972), 10521062.
2. James, I. M., On H-spaces and their homotopy groups, Quart. J. Math. Oxford Ser. 11 (1960), 161179.
3. Kahn, D. W., Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432450.
4. Stasheff, J. D., On extensions of Espaces, Trans. Amer. Math. Soc. 105 (1962), 126135.
5. Stasheff, J. D., H-space problems, H-spaces, Neuchâtel (Suisse), Août 1970 (Springer-Verlag Notes, Vol. 196) 122136.
6. Williams, F. D., Quasi-commutativity of H-spaces, Michigan Math. J. 19 (1972), 209213.
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H-Equivalence Classes of Multiplications on Certain Fiber Spaces

  • Chao-Kun Cheng (a1)

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