On the group of real analytic diffeomorphisms

Tsuboi, Takashi

doi:10.24033/asens.2104

On the group of real analytic diffeomorphisms
[Sur le groupe des difféomorphismes analytiques réels]

Tsuboi, Takashi

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 601-651.

Résumé
Abstract

Le groupe des difféomorphismes analytiques réels d’une variété analytique réelle est un groupe riche. Il est dense dans le groupe des difféomorphismes lisses. Herman a montré que, pour le tore de dimension $n$ , sa composante connexe de l’identité est un groupe simple. Pour les variétés $U (1)$ fibrées, pour les variétés admettant une action semi-libre spéciale de $U (1)$ , et pour les variétés de dimension $2$ ou $3$ admettant une action non-triviale de $U (1)$ , on montre que la composante de l’identité du groupe des difféomorphismes analytiques réels est un groupe parfait.

The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the $n$ -dimensional torus, its identity component is a simple group. For $U (1)$ fibered manifolds, for manifolds admitting special semi-free $U (1)$ actions and for 2- or 3-dimensional manifolds with nontrivial $U (1)$ actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

Zbl

DOI : 10.24033/asens.2104

Classification : 57R52, 57R50, 58A07, 58F18, 57R30, 53C12, 58C15, 37C05
Keywords: diffeomorphism groups, foliations, real analytic, rotations,

U (1)

action, circle bundles
Mot clés : groupes de difféomorphismes, feuilletages, analytique réel, rotations, action de

U (1)

, fibrés en cercle

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     author = {Tsuboi, Takashi},
     title = {On the group of real analytic diffeomorphisms},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {601--651},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 42},
     number = {4},
     year = {2009},
     doi = {10.24033/asens.2104},
     zbl = {1181.58009},
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     url = {https://www.numdam.org/articles/10.24033/asens.2104/}
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Tsuboi, Takashi. On the group of real analytic diffeomorphisms. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 601-651. doi : 10.24033/asens.2104. https://www.numdam.org/articles/10.24033/asens.2104/

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