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Comptes Rendus Mathématique
Volume 341, n° 1
pages 29-34 (juillet 2005)
Doi : 10.1016/j.crma.2005.06.002
Received : 24 May 2005 ;  accepted : 28 May 2005
Quasi-morphisme de Calabi sur les surfaces de genre supérieur
Calabi quasi-morphism on higher genus surfaces
 

Pierre Py
Unité de mathématiques pures et appliquées, École normale supérieure de Lyon, UMR 5669 CNRS, 46, allée dʼItalie, 69364 Lyon cedex 07, France 

Résumé

Nous construisons un quasi-morphisme homogène   sur le groupe des difféomorphismes hamiltoniens dʼune surface (fermée, connexe, orientée) de genre supérieur ou égal à 2, ayant la propriété suivante. Si U est un ouvert connexe de S difféomorphe à un disque ou à un anneau, la restriction de   au sous-groupe formé des difféomorphismes qui sont le temps 1 dʼune isotopie hamiltonienne dans U , est égale au morphisme de Calabi. Pour citer cet article : P. Py, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

We construct a homogeneous quasi-morphism   on the group of Hamiltonian diffeomorphisms of a (closed, connected, oriented) surface S of genus greater or equal to 2, with the following property. For each connected open set U in S diffeomorphic to a disk or to an annulus, the restriction of   to the subgroup of diffeomorphisms which are the time 1 map of a Hamiltonian isotopy in U , equals Calabiʼs homomorphism. To cite this article: P. Py, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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