1994
DOI: 10.4153/cjm-1994-037-0
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Co-H-Structures on Moore Spaces of Type (G, 2)

Abstract: We consider the set (of homotopy classes) of co-H-structures on a Moore space M(G,n), where G is an abelian group and n is an integer ≥ 2. It is shown that for n > 2 the set has one element and for n = 2 the set is in one-one correspondence with Ext(G, G ⊗ G). We make a detailed investigation of the co-H-structures on M(G, 2) in the case G = ℤm, the integers mod m. We give a specific indexing of the co-H-structures on M(ℤm, 2) and of the homotopy classes of maps from M(ℤm, 2) to M(ℤn, 2) by means of certain… Show more

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Cited by 13 publications
(35 citation statements)
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“…This co-H structure is unique [4]. Thus the composite with Σϕ is a co-H map, and the assertion follows from Corollary 3.2.…”
Section: On Certain Co-h Spaces Related To Moore Spaces 3091mentioning
confidence: 67%
See 1 more Smart Citation
“…This co-H structure is unique [4]. Thus the composite with Σϕ is a co-H map, and the assertion follows from Corollary 3.2.…”
Section: On Certain Co-h Spaces Related To Moore Spaces 3091mentioning
confidence: 67%
“…Hence it is a suspension, and so homotopy co-associative. If n ≥ 2 it is a double suspension, and the homotopy co-commutativity for n = 1 was proved in [4]. So suppose the assertion holds for k − 1, k ≥ 1.…”
Section: On Certain Co-h Spaces Related To Moore Spaces 3091mentioning
confidence: 96%
“…Let RP b a = RP b /RP a−1 and let X n be the nconnected cover of a space X. According to [20], the homotopy fibre of the inclusion P 3 (2) ⊂ ✲ BSO(3) is ΣRP 4 2 ∨ P 6 (2) and so there is a fibre sequence SO(3) ✲ ΣRP 4 2 ∨ P 6 (2) ✲ P 3 (2). It follows that there is a fibre sequence Ω(P 3 (2) 2 ) ∂ ✲ S 3 ✲ ΣRP 4 2 ∨ P 6 (2) ✲ P 3 (2) 2 , where the map S 3 → ΣRP 4 2 ∨ P 6 (2) is of degree 4 into the bottom cell of target space.…”
Section: Introductionmentioning
confidence: 99%
“…Assertion (1) follows from some standard arguments in homotopy theory. We introduce "combinatorial calculations" for the Hopf map to prove assertion (2). These combinatorial methods were introduced by Fred Cohen in [6] to attack the Barratt conjecture and have been applied to the James-Hopf maps [21].…”
Section: Introductionmentioning
confidence: 99%
“…The results of Section 5 are applied here to compute an explicit formula of the element c A from a free resolution of A (Theorem 7.5). In this way we show that if A is finitely generated, then c A is trivial if and only if A has an element of order 2 (Corollary 7.6), generalizing a result of Arkowitz and Golasiński ( [2]) for cyclic groups.…”
Section: Introductionmentioning
confidence: 99%