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 -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial 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 , sa composante connexe de l’identité est un groupe simple. Pour les variétés fibrées, pour les variétés admettant une action semi-libre spéciale de , et pour les variétés de dimension ou admettant une action non-triviale de , on montre que la composante de l’identité du groupe des difféomorphismes analytiques réels est un groupe parfait.
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
@article{ASENS_2009_4_42_4_601_0, 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 = {http://www.numdam.org/articles/10.24033/asens.2104/} }
TY - JOUR AU - Tsuboi, Takashi TI - On the group of real analytic diffeomorphisms JO - Annales scientifiques de l'École Normale Supérieure PY - 2009 SP - 601 EP - 651 VL - 42 IS - 4 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2104/ DO - 10.24033/asens.2104 LA - en ID - ASENS_2009_4_42_4_601_0 ER -
%0 Journal Article %A Tsuboi, Takashi %T On the group of real analytic diffeomorphisms %J Annales scientifiques de l'École Normale Supérieure %D 2009 %P 601-651 %V 42 %N 4 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2104/ %R 10.24033/asens.2104 %G en %F ASENS_2009_4_42_4_601_0
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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