On the group of real analytic diffeomorphisms  [ Sur le groupe des difféomorphismes analytiques réels ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 4, pp. 601-651.

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.

DOI : https://doi.org/10.24033/asens.2104
Classification : 57R52,  57R50,  58A07,  58F18,  57R30,  53C12,  58C15,  37C05
Mots 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},
     language = {en},
     url = {www.numdam.org/item/ASENS_2009_4_42_4_601_0/}
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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. http://www.numdam.org/item/ASENS_2009_4_42_4_601_0/

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