Geodesic
On the Mapping Theorem for Lusternik-Schnirelmann Category II
Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1389-1398

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

Let X and Y be 1-connected spaces having the homotopy type of cw-complexes. Definition 0.1. A continuous map f:X → Y is Ω-split if Ωf:ΩX → ΩY admits a retraction up to homotopy.In [6] we prove the following “mapping theorem”:THEOREM 0.1. (a) If f is Ω-split, then cat(X) ≦ cat(Y);(b) If π*(f) is split injective and ΩY has the homotopy type of a product of Eilenberg-MacLane spaces, then f is Ω-split. 
Félix, Yves; Lemaire, Jean-Michel. On the Mapping Theorem for Lusternik-Schnirelmann Category II. Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1389-1398. doi: 10.4153/CJM-1988-062-0
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