Rationalized evaluation subgroups of a map I: Sullivan models, derivations and [formula omitted]-sequences

Abstract

We identify the homomorphism induced on rational homotopy groups by the evaluation map ω : map ( X , Y ; f ) → Y in terms of a map of complexes of derivations constructed directly from the Sullivan minimal model of f . This allows us to characterize the rationalized n th evaluation subgroup of f and, more generally, the rationalization of the so-called G -sequence of the map f . We use these results to study the G -sequence in the context of rational homotopy theory.