Subgroups of continuous groups acting differentiably on the half-line
Plante, Joseph F.
Annales de l'Institut Fourier, Tome 34 (1984), p. 47-56 / Harvested from Numdam
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Nous considérons des groupes de différomorphismes de la demi-droite fermée qui ne fixe qu’un point. Un tel groupe, s’il est un groupe de Lie, est isomorphe à un sous-groupe du groupe affine. D’autre part, un tel groupe, s’il est isomorphe à un sous-groupe discret d’un groupe de Lie résoluble, est topologiquement équivalent à un sous-groupe du groupe affine.

We consider groups of diffeomorphisms of the closed half-line which fix only the end point. When the group is a Lie group it is isomorphic to a subgroup of the affine group. On the other hand, when the group is isomorphic to a discrete subgroup of a solvable Lie group it is topologically equivalent to a subgroup of the affine group.

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     author = {Plante, Joseph F.},
     title = {Subgroups of continuous groups acting differentiably on the half-line},
     journal = {Annales de l'Institut Fourier},
     volume = {34},
     year = {1984},
     pages = {47-56},
     doi = {10.5802/aif.950},
     mrnumber = {86j:58020},
     zbl = {0519.57037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1984__34_1_47_0}
}

Plante, Joseph F. Subgroups of continuous groups acting differentiably on the half-line. Annales de l'Institut Fourier, Tome 34 (1984) pp. 47-56. doi : 10.5802/aif.950. http://gdmltest.u-ga.fr/item/AIF_1984__34_1_47_0/

[1] Campbell, Continuous groups, Chelsea, New York (1966).

[2] G. Chatelet, Sur les feuilletages induits par l'action de groupes de Lie nilpotents, Ann. Inst. Fourier, 27-2 (1977), 161-190. | Numdam | MR 57 #17662 | Zbl 0349.57009

[3] A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl., (9) 11 (1932), 333-375. | JFM 58.1124.04

[4] G. Hector, On manifolds foliated by nilpotent Lie group actions, preprint Lille (1980).

[5] N. Kopell, Commuting diffeomorphisms, Proc. Symposia Pure Math., v. 14, A.M.S., (1969), 165-184. | MR 42 #5285 | Zbl 0225.57020

[6] J. Milnor, On fundamental groups of complete affinely flat manifolds, Adv. Math., 25 (1977), 178-187. | MR 56 #13130 | Zbl 0364.55001

[7] J. Plante, Foliations with measure preserving holonomy, Ann. Math., 102 (1975), 327-361. | MR 52 #11947 | Zbl 0314.57018

[8] J. Plante, Solvable groups acting on this line, Trans. A.M.S., 278 (1983), 401-414. | MR 85b:57048 | Zbl 0569.57012

[9] J. Plante, W. Thurston, Polynomial growth in holonomy groups of foliations, Comm. Math. Helv., 39 (51) (1976), 567-584. | MR 55 #9117 | Zbl 0348.57009

[10] W. Thurston, A generalization of the Reeb Stability Theorem, Topology, 13 (1974), 347-352. | MR 50 #8558 | Zbl 0305.57025

[11] J. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geom., 2 (1968), 421-446. | MR 40 #1939 | Zbl 0207.51803