Abstract
A l'aide du calcul differentiel de Fox, on definit, pour tout entier positif k, une application sur le groupe d'homeotopie M g,1 d'une surface de genre g et de bord a une composante, qui coincide avec le k + 1 eme homomorphisme de Johnson-Morita quand on la restreint a un sous-grimpe approprie. Ceci permet d'obtenir de facon tres simple une extension homomorphe des deuxieme et troisieme homomorphismes de Johnson-Morita a tout le groupe M g,1 .
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