Homomorphic extensions of Johnson homomorphisms via Fox calculus
Annales de l'Institut Fourier, Volume 54 (2004) no. 4, p. 1073-1106
Using Fox differential calculus, for any positive integer k, we construct a map on the mapping class group 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 g,1 of the second and third Johnson-Morita homomorphisms.
A l’aide du calcul différentiel de Fox, on définit pour tout entier positif k, une application sur le groupe d’homéotopie 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 g,1
DOI : https://doi.org/10.5802/aif.2044
Classification:  57M05
Keywords: mapping class group of a surface, Johnson-Morita homomorphisms, Fox differential calculus
@article{AIF_2004__54_4_1073_0,
     author = {Perron, Bernard},
     title = {Homomorphic extensions of Johnson homomorphisms via Fox calculus},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {4},
     year = {2004},
     pages = {1073-1106},
     doi = {10.5802/aif.2044},
     mrnumber = {2111022},
     zbl = {02162420},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2004__54_4_1073_0}
}
Homomorphic extensions of Johnson homomorphisms via Fox calculus. Annales de l'Institut Fourier, Volume 54 (2004) no. 4, pp. 1073-1106. doi : 10.5802/aif.2044. https://aif.centre-mersenne.org/item/AIF_2004__54_4_1073_0/

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