2015/12/01 by Schwass, James
#55S37 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1512.00357
A phantom map is a potentially nontrivial map which induces the zero map on every homology theory and on homotopy groups. Zabrodsky has shown that in the presence of particular finiteness conditions on spaces X and Y every map X→ Y is a phantom map. More specifically, Zabrodsky essentially requires Y to be a finite CW complex and X to be a Postnikov space. We show Zabrodsky's observations hold under less restrictive finiteness conditions on the spaces X and Y, making use of the Zabrodsky lemma and the machinery of resolving classes. As an application we identify, up to extension, the group of self-homotopy equivalences of spaces belonging to a particular family.