The rational homotopy Lie algebra of function spaces

@article{Martn2008TheRH,
  title={The rational homotopy Lie algebra of function spaces},
  author={Urtzi Buijs Mart{\'i}n and Aniceto Murillo Mas},
  journal={Commentarii Mathematici Helvetici},
  year={2008},
  volume={83},
  pages={723-739}
}
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 p*(Y) 
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