[Actions analytiques réelles, conservant le volume, de réseaux sur les variétés de dimension 4]
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 -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.
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@article{CRMATH_2002__334_11_1011_0,
author = {Farb, Benson and Shalen, Peter B.},
title = {Real-analytic, volume-preserving actions of lattices on 4-manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {1011--1014},
publisher = {Elsevier},
volume = {334},
number = {11},
year = {2002},
doi = {10.1016/S1631-073X(02)02347-6},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02347-6/}
}
TY - JOUR AU - Farb, Benson AU - Shalen, Peter B. TI - Real-analytic, volume-preserving actions of lattices on 4-manifolds JO - Comptes Rendus. Mathématique PY - 2002 SP - 1011 EP - 1014 VL - 334 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02347-6/ DO - 10.1016/S1631-073X(02)02347-6 LA - en ID - CRMATH_2002__334_11_1011_0 ER -
%0 Journal Article %A Farb, Benson %A Shalen, Peter B. %T Real-analytic, volume-preserving actions of lattices on 4-manifolds %J Comptes Rendus. Mathématique %D 2002 %P 1011-1014 %V 334 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02347-6/ %R 10.1016/S1631-073X(02)02347-6 %G en %F CRMATH_2002__334_11_1011_0
Farb, Benson; Shalen, Peter B. Real-analytic, volume-preserving actions of lattices on 4-manifolds. Comptes Rendus. Mathématique, Tome 334 (2002) no. 11, pp. 1011-1014. doi : 10.1016/S1631-073X(02)02347-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02347-6/
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