Geodesic
Co-H-Structures on Moore Spaces of Type (G, 2)
Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 673-686

Voir la notice de l'article provenant de la source Cambridge University Press

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 standard homotopy elements. In terms of this indexing we completely determine the co-H-maps from M{Zm , 2) to M(Zn , 2) for each co-H-structure on M(Zm , 2) and on M(Zn , 2). This enables us to describe the action of the group of homotopy equivalences of M(Zn , 2) on the set of co-H-structures of M(Zm , 2). We prove that the action is transitive. From this it follows that if m is odd, all co-H-structures on M(Zm , 2) are associative and commutative, and if m is even, all co-H-structures on M(Zm , 2) are associative and non-commutative.
DOI : 10.4153/CJM-1994-037-0
Mots-clés : 55P45, 55P40 
Arkowitz, Martin; Golasinski, Marek. Co-H-Structures on Moore Spaces of Type (G, 2). Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 673-686. doi: 10.4153/CJM-1994-037-0
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