Subgroups of continuous groups acting differentiably on the half-line

Joseph F. Plante

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 1, page 47-56
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Plante, Joseph F.. "Subgroups of continuous groups acting differentiably on the half-line." Annales de l'institut Fourier 34.1 (1984): 47-56. <http://eudml.org/doc/74621>.

@article{Plante1984,
abstract = {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.},
author = {Plante, Joseph F.},
journal = {Annales de l'institut Fourier},
keywords = {groups of diffeomorphisms of the closed half-line which fix only the end point; subgroup of the affine group; discrete subgroup of a solvable Lie group},
language = {eng},
number = {1},
pages = {47-56},
publisher = {Association des Annales de l'Institut Fourier},
title = {Subgroups of continuous groups acting differentiably on the half-line},
url = {http://eudml.org/doc/74621},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Plante, Joseph F.
TI - Subgroups of continuous groups acting differentiably on the half-line
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 1
SP - 47
EP - 56
AB - 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.
LA - eng
KW - groups of diffeomorphisms of the closed half-line which fix only the end point; subgroup of the affine group; discrete subgroup of a solvable Lie group
UR - http://eudml.org/doc/74621
ER -

References

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  1. [1] CAMPBELL, Continuous groups, Chelsea, New York (1966). 
  2. [2] G. CHATELET, Sur les feuilletages induits par l'action de groupes de Lie nilpotents, Ann. Inst. Fourier, 27-2 (1977), 161-190. Zbl0349.57009MR57 #17662
  3. [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. Zbl58.1124.04JFM58.1124.04
  4. [4] G. HECTOR, On manifolds foliated by nilpotent Lie group actions, preprint Lille (1980). 
  5. [5] N. KOPELL, Commuting diffeomorphisms, Proc. Symposia Pure Math., v. 14, A.M.S., (1969), 165-184. Zbl0225.57020MR42 #5285
  6. [6] J. MILNOR, On fundamental groups of complete affinely flat manifolds, Adv. Math., 25 (1977), 178-187. Zbl0364.55001MR56 #13130
  7. [7] J. PLANTE, Foliations with measure preserving holonomy, Ann. Math., 102 (1975), 327-361. Zbl0314.57018MR52 #11947
  8. [8] J. PLANTE, Solvable groups acting on this line, Trans. A.M.S., 278 (1983), 401-414. Zbl0569.57012MR85b:57048
  9. [9] J. PLANTE, W. THURSTON, Polynomial growth in holonomy groups of foliations, Comm. Math. Helv., 39 (51) (1976), 567-584. Zbl0348.57009MR55 #9117
  10. [10] W. THURSTON, A generalization of the Reeb Stability Theorem, Topology, 13 (1974), 347-352. Zbl0305.57025MR50 #8558
  11. [11] J. WOLF, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geom., 2 (1968), 421-446. Zbl0207.51803MR40 #1939

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