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Astérisque - Titles - 390 (2017) 65-75

Titles < 2017 < 390

Séminaire Bourbaki, volume 2015/2016, exposés 1104-1119
Astérisque 390 (2017), xi+533 pages
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Presentation, Summary

Exposé 1106 : Conjecture de Hilbert-Smith en dimension 3
Sylvain MAILLOT
Astérisque 390 (2017), 65-75
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Résumé :
La conjecture de Hilbert-Smith en dimension n affirme que, si G est un groupe topologique localement compact qui admet une injection continue dans le groupe d'homéomorphismes d'une variété connexe de dimension n, alors G est un groupe de Lie. Nous décrirons la preuve du cas n=3, due à J. Pardon. Cette preuve utilise des outils divers tels que l'homologie de Čech, la topologie des variétés de dimension 3, la théorie des surfaces minimales et des résultats de J. Nielsen sur les groupes modulaires des surfaces hyperobliques.

Mots-clefs : Groupes de transformations, conjecture de Hilbert-Smith, 5ème problème de Hilbert, variété de dimension 3, variétés ouvertes.

Abstract:
Exposé 1106 : The Hilbert-Smith conjecture in dimension 3
The Hilbert-Smith conjecture in dimension n states that if a locally compact topological group G admits a continuous injection into the homeomorphism group of some connected n-manifold M, then G is a Lie group. We will discuss J. Pardon's proof of this conjecture for n=3. This proof uses various tools, including Čech homology, 3-manifold topology, minimal surface theory and results of J. Nielsen on the mapping class groups of hyperbolic surfaces.

Keywords: Transformation groups, Hilbert-Smith conjecture, Hilbert's 5th problem, 3-manifolds, open manifolds.

Class. math. : 57S10, 57M60, 57S05, 57N10, 54H15, 55M35.


ISSN : 0303-1179
Publié avec le concours de : Centre National de la Recherche Scientifique

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