Rationalized evaluation subgroups of a map II: Quillen models and adjoint maps

Abstract

We identify the long exact sequence induced on rational homotopy groups by the evaluation map ω : map ( X , Y ; f ) → Y , and in particular the rationalization of the evaluation subgroups of f , in terms of derivations of Quillen models and adjoint maps. We consider a generalization of a question of Gottlieb within the context of rational homotopy theory. We also study the rationalization of the G -sequence of a map. In a separate result of independent interest, we give an explicit Quillen minimal model of a product A × X , in the case in which A is a rational co- H -space.