[Sur la structure et l'arithméticité des groupes enveloppant un réseau]
Nous nous intéressons à l'ensemble des plongements possibles d'un groupe dénombrable comme réseau dans un groupe localement compact. Pour une grande classe de groupes dénombrables, nous annonçons des résultats de structure et d'arithméticité de tels plongements. Cette classe contient tous les groupes linéaires dont l'adhérence de Zariski est simple, les groupes dont le premier nombre de Betti est non nul, les groupes hyperboliques acylindriques et les groupes de convergence.
We announce results about the structure and arithmeticity of all possible lattice embeddings of a class of countable groups that encompasses all linear groups with simple Zariski closure, all groups with non-vanishing first -Betti number, non-elementary acylindrically hyperbolic groups, and non-elementary convergence groups.
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@article{CRMATH_2015__353_5_409_0,
author = {Bader, Uri and Furman, Alex and Sauer, Roman},
title = {On the structure and arithmeticity of lattice envelopes},
journal = {Comptes Rendus. Math\'ematique},
pages = {409--413},
publisher = {Elsevier},
volume = {353},
number = {5},
year = {2015},
doi = {10.1016/j.crma.2015.02.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.02.010/}
}
TY - JOUR AU - Bader, Uri AU - Furman, Alex AU - Sauer, Roman TI - On the structure and arithmeticity of lattice envelopes JO - Comptes Rendus. Mathématique PY - 2015 SP - 409 EP - 413 VL - 353 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.02.010/ DO - 10.1016/j.crma.2015.02.010 LA - en ID - CRMATH_2015__353_5_409_0 ER -
%0 Journal Article %A Bader, Uri %A Furman, Alex %A Sauer, Roman %T On the structure and arithmeticity of lattice envelopes %J Comptes Rendus. Mathématique %D 2015 %P 409-413 %V 353 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.02.010/ %R 10.1016/j.crma.2015.02.010 %G en %F CRMATH_2015__353_5_409_0
Bader, Uri; Furman, Alex; Sauer, Roman. On the structure and arithmeticity of lattice envelopes. Comptes Rendus. Mathématique, Tome 353 (2015) no. 5, pp. 409-413. doi : 10.1016/j.crma.2015.02.010. http://www.numdam.org/articles/10.1016/j.crma.2015.02.010/
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☆ This project was supported in part by ERC grant 306706 (U.B.), BSF grant 2008267 (U.B. and A.F.), and NSF grant DMS 1207803 (A.F.).
