Phantom maps and rational homotopy

TL;DR

This paper extends existing theorems linking phantom maps to rational homotopy theory, providing new examples and calculations of homotopy sets of phantom maps and special phantom maps.

Contribution

It generalizes prior theorems and offers new computational methods and examples for homotopy sets involving phantom maps.

Findings

New calculations of homotopy sets Ph(X, Y) of phantom maps

Identification of subsets SPh(X, Y) of special phantom maps

Extended theorems relating phantom maps to rational homotopy

Abstract

We generalize theorems of McGibbon-Roitberg, Iriye, and Meier on the relations between phantom maps and rational homotopy, and apply them to provide new calculational examples of the homotopy sets Ph(X, Y ) of phantom maps and the subsets SPh(X, Y ) of special phantom maps.