On exterior $A\sb n$-spaces and modified projective spaces

On mod p Ap–spaces

“…Theorem 4.5 (Theorem 1.2 in [12], also see Section 8 in [13]) Let X be a homotopy H -space with H * (X; Z/3Z) being finite. Then for any n ∈ Z with n ≡ 0 mod 3 and n > 3, if (4-1) QH 2(3 a ·2t)−1 (X, Z/3Z) = 0, for t ≥ n − 1, then we have (4-2) P 3 a : QH 2(3 a (n−2))−1 (X, Z/3Z) → QH 2(3 a n)−1 (X, Z/3Z)…”

“…R. Harper for suggesting the reference [12] and valuable knowledge about H -space of rank p and higher associativity. We wish to thank the referee most warmly for his/her suggestions and comments on using the modified projective space of Hemmi [13] which has essentially improved the article, and also the careful reading of our manuscript. We are also indebted to Prof. Jérôme Scherer and Prof. Fred Cohen for careful reading of the manuscript and many valuable suggestions which have improved the paper.…”

Higher homotopy commutativity and cohomology of finite H–spaces

“…In the proof of Theorem 2.2 (2), we do not need the condition (2)(3)(4)(5)(6)(7)(8)(9)(10). In fact, the proof of Theorem 2.2 (2) shows that if X is an A n+1 -space and there is a family of maps {ψ i } 1≤i≤n with the conditions (2-8)-(2-9), then there is a family of maps {Q i } 1≤i≤n with the conditions (2-5)-(2-7).…”

“…Theorem A (1) has been already proved for a special case or under additional hypotheses: for p = 3 by Hemmi [7, Theorem 1.1] and for p ≥ 5 by Lin [19,Theorem B] under the hypotheses that the space admits an AC p−1 -space structure and the mod p cohomology is A p -primitively generated (see Hemmi [8] and Lin [19]).…”

“…Hemmi [8] modified the construction of the projective space P p (X) to get the algebra T [p+1] [y 1 , . .…”