Area functionals and Godbillon-Vey cocycles

Tsuboi, Takashi

Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 421-447.

Nous étudions le domaine naturel de définition de la classe de cohomologie de dimension 2 de Godbillon-Vey du groupe des difféomorphismes du cercle. On introduit la notion de fonctionnelle d’aire sur un espace de fonctions sur le cercle, on définit un espace suffisamment grand de fonctions sur le cercle avec fonctionnelle d’aire non triviale et on définit un groupe suffisamment grand d’homéomorphismes lipschitziens du cercle où la classe de Godbillon-Vey est définie.

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.

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