Localization, completion and detecting equivariant maps on skeletons
The authors extend results on phantom maps obtained by \textit{A. Zabrodsky} [Isr. J. Math. 58, 129-143 (1987; Zbl 0638.55020)] and the authors themselves [Publ. Res. Inst. Math. Sci. 24, 811-820 (1988; Zbl 0663.55006)] to results on so-called G-phantom maps in the category of equivariant spaces with base point. If f,g: \(X\to Y\) are two G-maps on a G-CW-complex, then f is called a G-phantom map when \(f/X^ n\) and \(g/X^ n\) are G-homotopic for all \(n\geq 0\). The authors give conditions under which G-maps induce injective maps between homotopy sets, and use this result, some consequences of it, and relations between the localization and the completion to characterize maps which are homotopic on skeletons.
equivariant unstable homotopy spectral sequence
scientific article; zbMATH DE number 4144941
scientific article