On the fundamental group of a mapping space. An example
Compositio Mathematica, Tome 28 (1974) no. 1, pp. 33-36. 
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Hansen, Vagn Lundsgaard. On the fundamental group of a mapping space. An example. Compositio Mathematica, Tome 28 (1974) no. 1, pp. 33-36. http://archive.numdam.org/item/CM_1974__28_1_33_0/

[1] H. Federer: A study of function spaces by spectral sequences. Trans. Amer. Math. Soc. 82 (1956) 340-361. | MR | Zbl

[2] S.T. Hu: Homotopy Theory. Academic Press, 1959. | MR | Zbl

[3] E.H. Spanier: Algebraic Topology. McGraw-Hill, 1966. | MR | Zbl

[4] R. Thom: L'homologie des espaces fonctionnels. Colloque de topologie algébrique, Louvain 1956. Thone, Liège; Masson, Paris, 1957, pp. 29-39. | MR | Zbl