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

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中文翻译：

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相对幻影映射和有理同伦

摘要：我们将 Gray 和 McGibbon-Roitberg 关于幻影映射和有理同伦关系的一些结果推广到相对幻影映射。由于 $\underset {\longleftarrow }{\mathrm {lim}}^{1}$ 和 profinite 补全技术不适用于相对幻影地图，我们开发了新技术。

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