On the group of real analytic diffeomorphisms

Takashi Tsuboi

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 4, page 601-651
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Tsuboi, Takashi. "On the group of real analytic diffeomorphisms." Annales scientifiques de l'École Normale Supérieure 42.4 (2009): 601-651. <http://eudml.org/doc/272143>.

@article{Tsuboi2009,
abstract = {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.},
author = {Tsuboi, Takashi},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {diffeomorphism groups; foliations; real analytic; rotations; $U(1)$ action; circle bundles},
language = {eng},
number = {4},
pages = {601-651},
publisher = {Société mathématique de France},
title = {On the group of real analytic diffeomorphisms},
url = {http://eudml.org/doc/272143},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Tsuboi, Takashi
TI - On the group of real analytic diffeomorphisms
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 4
SP - 601
EP - 651
AB - 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.
LA - eng
KW - diffeomorphism groups; foliations; real analytic; rotations; $U(1)$ action; circle bundles
UR - http://eudml.org/doc/272143
ER -

References

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