Comptes Rendus
no. 11
Real-analytic, volume-preserving actions of lattices on 4-manifolds
[Actions analytiques réelles, conservant le volume, de réseaux sur les variétés de dimension 4]
Benson Farb1 ; Peter B. Shalen2
1 Dept. of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA
2 Dept. of Mathematics, University of Illinois at Chicago, Chicago, IL 60680, USA
Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 1011-1014.

Soit Γ un réseau dans un groupe de Lie linéaire simple, dont le rang rationnel est supérieur ou égal à 7, et soit M une variété fermée de dimension 4 dont la caractéristique d'Euler–Poincaré est non nulle. Nous montrons que toute action analytique réelle de Γ sur M, qui conserve le volume, se factorise à travers l'action d'un groupe fini.

We prove that if Γ is a lattice of Q-rank at least 7 in a simple linear Lie group, then any real-analytic, volume-preserving action of Γ on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02347-6

Benson Farb 1 ; Peter B. Shalen 2

1 Dept. of Mathematics, University of Chicago, 5734 University Ave., Chicago, IL 60637, USA
2 Dept. of Mathematics, University of Illinois at Chicago, Chicago, IL 60680, USA 
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Benson Farb; Peter B. Shalen. Real-analytic, volume-preserving actions of lattices on 4-manifolds. Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 1011-1014. doi : 10.1016/S1631-073X(02)02347-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02347-6/

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