On the group of real analytic diffeomorphisms
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, pp. 601-651.

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.

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.

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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Tsuboi, Takashi. On the group of real analytic diffeomorphisms. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 42 (2009) no. 4, pp. 601-651. doi : 10.24033/asens.2104. http://www.numdam.org/articles/10.24033/asens.2104/

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