A BASED FEDERER SPECTRAL SEQUENCE AND THE RATIONAL HOMOTOPY OF FUNCTION-SPACES

We study the rational homotopy of function spaces within the context o f Quillen's minimal models. Our method is to consider a spectral seque nce with E-2(p,q) = (H) over tilde(q)(X,pi(p+q)(Y) x Q) converging to the rational homotopy groups of components of the based function space M(X, Y). Our results include calculations of rational homotopy group s as well as general contributions to the rational classification prob lem for components of function spaces.