logo École polytechnique
logo Journal de l'École Polytechnique
On closed subgroups of the group of homeomorphisms of a manifold
Frédéric Le Roux1
1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Pierre et Marie Curie 4, place Jussieu, Case 247, 75252 Paris Cedex 5, France
Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 147-159.

Let M be a triangulable compact manifold. We prove that, among closed subgroups of Homeo 0 (M) (the identity component of the group of homeomorphisms of M), the subgroup consisting of volume preserving elements is maximal.

Soit M une variété triangulable compacte. Nous montrons que, parmi les sous-groupes de Homeo 0 (M) (composante connexe de l’identité du groupe des homéomorphismes de M), le sous-groupe des homéomorphismes préservant le volume est maximal.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.7
Classification: 57S05, 57M60, 37E30
Keywords: Transformation groups, homeomorphisms, maximal closed subgroups
Mot clés : Groupes de transformations, homéomorphismes, sous-groupes fermés maximaux

Frédéric Le Roux 1

1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Pierre et Marie Curie 4, place Jussieu, Case 247, 75252 Paris Cedex 5, France
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{JEP_2014__1__147_0,
     author = {Fr\'ed\'eric Le Roux},
     title = {On closed subgroups of the group of homeomorphisms of a manifold},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {147--159},
     publisher = {\'Ecole polytechnique},
     volume = {1},
     year = {2014},
     doi = {10.5802/jep.7},
     mrnumber = {3322786},
     zbl = {1309.57027},
     language = {en},
     url = {https://jep.centre-mersenne.org/articles/10.5802/jep.7/}
}
TY  - JOUR
AU  - Frédéric Le Roux
TI  - On closed subgroups of the group of homeomorphisms of a manifold
JO  - Journal de l’École polytechnique — Mathématiques
PY  - 2014
SP  - 147
EP  - 159
VL  - 1
PB  - École polytechnique
UR  - https://jep.centre-mersenne.org/articles/10.5802/jep.7/
DO  - 10.5802/jep.7
LA  - en
ID  - JEP_2014__1__147_0
ER  - 
%0 Journal Article
%A Frédéric Le Roux
%T On closed subgroups of the group of homeomorphisms of a manifold
%J Journal de l’École polytechnique — Mathématiques
%D 2014
%P 147-159
%V 1
%I École polytechnique
%U https://jep.centre-mersenne.org/articles/10.5802/jep.7/
%R 10.5802/jep.7
%G en
%F JEP_2014__1__147_0
Frédéric Le Roux. On closed subgroups of the group of homeomorphisms of a manifold. Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 147-159. doi : 10.5802/jep.7. https://jep.centre-mersenne.org/articles/10.5802/jep.7/

[Bes04] M. Bestvina - “Questions in geometric group theory, collected by M. Bestvina” (2004), http://www.math.utah.edu/~bestvina/eprints/questions-updated.pdf

[Bro62] M. Brown - “A mapping theorem for untriangulated manifolds”, in Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N.J., 1962, p. 92-94 | Zbl

[Fat80] A. Fathi - “Structure of the group of homeomorphisms preserving a good measure on a compact manifold”, Ann. Sci. École Norm. Sup. (4) 13 (1980) no. 1, p. 45-93 | DOI | Numdam | MR | Zbl

[Ghy01] É. Ghys - “Groups acting on the circle”, Enseign. Math. (2) 47 (2001) no. 3-4, p. 329-407 | MR | Zbl

[GM06] J. Giblin & V. Markovic - “Classification of continuously transitive circle groups”, Geom. Topol. 10 (2006), p. 1319-1346 | DOI | MR | Zbl

[GP75] C. Goffman & G. Pedrick - “A proof of the homeomorphism of Lebesgue-Stieltjes measure with Lebesgue measure”, Proc. Amer. Math. Soc. 52 (1975), p. 196-198 | DOI | MR | Zbl

[Kir69] R. C. Kirby - “Stable homeomorphisms and the annulus conjecture”, Ann. of Math. (2) 89 (1969), p. 575-582 | DOI | MR | Zbl

[KT13] F. Kwakkel & F. Tal - “Homogeneous transformation groups of the sphere” (2013), arXiv:1309.0179v1

[Nav07] A. Navas - Grupos de difeomorfismos del círculo, Ensaios Matemáticos, vol. 13, Sociedade Brasileira de Matemática, Rio de Janeiro, 2007 | MR | Zbl

[OU41] J. C. Oxtoby & S. M. Ulam - “Measure-preserving homeomorphisms and metrical transitivity”, Ann. of Math. (2) 42 (1941), p. 874-920 | DOI | MR | Zbl

[Qui82] F. Quinn - “Ends of maps. III. Dimensions 4 and 5”, J. Differential Geom. 17 (1982) no. 3, p. 503-521 | DOI | MR | Zbl

Cited by Sources: