On closed subgroups of the group of homeomorphisms of a manifold

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

Journal de l’École polytechnique — Mathématiques (2014)

  • Volume: 1, page 147-159
  • ISSN: 2270-518X

Abstract

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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.

How to cite

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Le Roux, Frédéric. "On closed subgroups of the group of homeomorphisms of a manifold." Journal de l’École polytechnique — Mathématiques 1 (2014): 147-159. <http://eudml.org/doc/275648>.

@article{LeRoux2014,
abstract = {Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $\mathrm\{Homeo\}_\{0\}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.},
affiliation = {Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Pierre et Marie Curie 4, place Jussieu, Case 247, 75252 Paris Cedex 5, France},
author = {Le Roux, Frédéric},
journal = {Journal de l’École polytechnique — Mathématiques},
keywords = {Transformation groups; homeomorphisms; maximal closed subgroups; transformation groups},
language = {eng},
pages = {147-159},
publisher = {École polytechnique},
title = {On closed subgroups of the group of homeomorphisms of a manifold},
url = {http://eudml.org/doc/275648},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Le Roux, Frédéric
TI - On closed subgroups of the group of homeomorphisms of a manifold
JO - Journal de l’École polytechnique — Mathématiques
PY - 2014
PB - École polytechnique
VL - 1
SP - 147
EP - 159
AB - Let $M$ be a triangulable compact manifold. We prove that, among closed subgroups of $\mathrm{Homeo}_{0}(M)$ (the identity component of the group of homeomorphisms of $M$), the subgroup consisting of volume preserving elements is maximal.
LA - eng
KW - Transformation groups; homeomorphisms; maximal closed subgroups; transformation groups
UR - http://eudml.org/doc/275648
ER -

References

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  8. F. Kwakkel, F. Tal, Homogeneous transformation groups of the sphere, (2013) 
  9. A. Navas, Grupos de difeomorfismos del círculo, 13 (2007), Sociedade Brasileira de Matemática, Rio de Janeiro Zbl1163.37002
  10. J. C. Oxtoby, S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920 Zbl0063.06074MR5803
  11. F. Quinn, Ends of maps. III. Dimensions 4 and 5 , J. Differential Geom. 17 (1982), 503-521 Zbl0533.57009MR679069

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