Some algebraic constructions in rational homotopy theory

In this note we describe constructions in the category of differential graded commutative algebras over the rational numbers Q which are analogs of the space F(X, Y) of continuous maps of X to Y, the component F(X, Y, f) containing f is an element of F(X, Y), fibrations, induced fibrations, the space Gamma(pi) of sections of a fibration pi:E --> X, and the component Gamma(pi, sigma) containing sigma is an element of Gamma(pi). As a focus, we address the problem of expressing pi*(F(X, Y, f)) = Hom(pi*(F(X, Y, f)), Q) in terms of differential graded algebra models for X and Y. (C) 1997 Elsevier Science B.V.