Morita, Shigeyuki
Families of jacobian manifolds and characteristic classes of surface bundles. I
Annales de l'institut Fourier, Tome 39 (1989) no. 3 , p. 777-810
Zbl 0672.57015 | MR 91d:32028 | 1 citation dans Numdam
doi : 10.5802/aif.1188
URL stable : http://www.numdam.org/item?id=AIF_1989__39_3_777_0

Dans notre travail précédent nous avons défini la notion de classes caractéristiques des fibrés en surface, qui sont des espaces fibrés différentiables dont les fibres sont des surfaces fermées orientées. Dans cet article nous dérivons de nouvelles relations entre ces classes caractéristiques en considérant un plongement canonique d’un fibré en surface donné avec section dans sa famille associée de variétés jacobiennes. Comme étape technique cruciale nous déterminons la première cohomologie du groupe de difféotopies d’une surface orientée à valeurs dans l’homologie de la surface. Ceci peut avoir un sens indépendant.
In our previous work we have defined the notion of characteristic classes of surface bundles, which are differentiable fibre bundles whose fibres are closed oriented surfaces. In this paper we derive new relations between these characteristic classes by considering a canonical embedding of a given surface bundle with cross section to its associated family of Jacobian manifolds. As a key technical step we determine the first cohomology group of the mapping class group of oriented surfaces with coefficients in the homology of the surface. This might have an independent meaning.

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