On the rational homotopy type of function spaces

The main result of this paper is the construction of a minimal model for the function space F(X,Y) of continuous functions from a finite type, finite dimensional space X to a finite type, nilpotent space Y in terms of minimal models for X and Y. For the component containing the constant map, pi*(F(X, Y)) x Q = pi*(Y) x H-*(X; Q) in positive dimensions. When X is formal, there is a simple formula for the differential of the minimal model in terms of the differential of the minimal model for Y and the coproduct of H*(X; Q). We also give a version of the main result for the space of cross sections of a fibration.