Displaying similar documents to “Partially defined cocycles and the Maslov index for a local ring”

Homomorphic extensions of Johnson homomorphisms via Fox calculus

Bernard Perron (2004)

Annales de l’institut Fourier

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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 + 1 t h 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.