Geodesic
Spaces of Maps into Eilenberg-Maclane Spaces
Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 782-785

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we provide alternative and unified proofs for two theorems on the homotopy groups of spaces of (continuous) maps into Eilenberg-MacLane spaces. The first theorem is due to Thorn, and independently Federer, and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, n) for n ≧ 1 with π abelian. The second theorem is due to Gottlieb and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, 1) with π nonabelian. As a main tool we shall use the homotopy sequences for certain fibrations of spaces of maps. 2. Basic notation and some preliminary remarks. For any pair of connected CW-complexes X and Y with base points, we denote by M(X, Y), respectively F(X, Y), the space of free maps, respectively based maps, of X into Y. 
Hansen, Vagn Lundsgaard. Spaces of Maps into Eilenberg-Maclane Spaces. Canadian journal of mathematics, Tome 33 (1981) no. 4, pp. 782-785. doi: 10.4153/CJM-1981-059-7
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