The rational homotopy Lie algebra of function spaces

Abstract

In this paper we fully describe the rational homotopy Lie algebra of any component of a given (free or pointed) function space. Also, we characterize higher order Whitehead products on these spaces. From this, we deduce the existence of H-structures on a given component of a pointed mapping space ℱ*(X,Y;f ) between rational spaces, assuming the cone length of X is smaller than the order of any non trivial generalized Whitehead product in π*(Y).