Relative phantom maps and rational homotopy

Abstract

We generalize some results of Gray and McGibbon-Roitberg on relations between phantom maps and rational homotopy to relative phantom maps. Since the l i m ⟵ 1 \underset {\longleftarrow }{\mathrm {lim}}^{1} and the profinite completion techniques do not apply to relative phantom maps, we develop new techniques.