Moore spaces in proper homotopy
In standard homotopy theory, Moore spaces exist and are unique. In proper homotopy, the existence of the proper analogues of Moore spaces are defined using, as homology, that with values in the category (tow-Ab, Ab) of towers of abelian groups given for instance by using the Edwards-Hastings embedding of the proper category into (two-Top, Top) and then using an ordinary homology functor. In this paper the authors show that proper Moore spaces exist, but need not be unique. The non-uniqueness results follow from the fact that the abelian category (tow-Ab, Ab) used has projective dimension two. Examples of non properly equivalent proper Moore spaces for the same tower of abelian groups are given.
scientific article; zbMATH DE number 895939