# The rational homotopy Lie algebra of function spaces

### Urtzi Buijs

Universidad de Málaga, Spain### Aniceto Murillo

Universidad de Málaga, Spain

## 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 $π_{∗}(Y)$.

## Cite this article

Urtzi Buijs, Aniceto Murillo, The rational homotopy Lie algebra of function spaces. Comment. Math. Helv. 83 (2008), no. 4, pp. 723–739

DOI 10.4171/CMH/141