Homomorphic extensions of Johnson homomorphisms via Fox calculus
[Extensions homomorphes des homomorphismes de Johnson via le calcul de Fox]
Perron, Bernard1
1 Université de Bourgogne, Institut de mathématiques de Bourgogne, UFR sciences et techniques, 9 avenue Alain Savary, BP 47870, 21078 Dijon cedex (France)
Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1073-1106.

A l’aide du calcul différentiel de Fox, on définit pour tout entier positif k, une application sur le groupe d’homéotopie ℳ g,1 d’une surface de genre g et de bord à une composante, qui coïncide avec le k+1 ème homomorphisme de Johnson- Morita quand on la restreint à un sous-groupe approprié. Ceci permet d’obtenir de façon très simple une extension homomorphe des deuxième et troisième homomorphismes de Johnson- Morita à tout le groupe ℳ g,1

Using Fox differential calculus, for any positive integer k, we construct a map on the mapping class group ℳ g,1 of a surface of genus g with one boundary component, such that, when restricted to an appropriate subgroup, it coincides with the k+1th Johnson-Morita homomorphism. This allows us to construct very easily a homomorphic extension to ℳ g,1 of the second and third Johnson-Morita homomorphisms.

DOI : 10.5802/aif.2044
Classification : 57M05
Keywords: mapping class group of a surface, Johnson-Morita homomorphisms, Fox differential calculus
Mot clés : groupe d'homéotopie d'une surface, homomorphismes de Johnson-Morita, calcul différentiel de Fox
Perron, Bernard 1

1 Université de Bourgogne, Institut de mathématiques de Bourgogne, UFR sciences et techniques, 9 avenue Alain Savary, BP 47870, 21078 Dijon cedex (France) 
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Perron, Bernard. Homomorphic extensions of Johnson homomorphisms via Fox calculus. Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1073-1106. doi : 10.5802/aif.2044. http://archive.numdam.org/articles/10.5802/aif.2044/

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