Group Theory
L2-Betti numbers of locally compact groups
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 339-342.

The present paper is a summary and overview of results obtained in the authorʼs thesis, “L2-Betti Numbers of Locally Compact Groups”, wherein the definition of L2-Betti numbers for countable groups is extended to locally compact unimodular groups. In many cases, the L2-Betti numbers of a lattice are proportional to those of the ambient locally compact group, yielding new results for certain classes of lattices, including arithmetic lattices and Kac–Moody lattices.

Cet article présente quelques résultats de la thèse de lʼauteur, « L2-Betti Numbers of Locally Compact Groups », dans laquelle la définition des nombres L2 de Betti des groupes dénombrables a été généralisée au cas des groupes localement compacts unimodulaires. Dans de nombreux cas, les nombres L2 de Betti dʼun réseau quelconque dans un groupe localement compact sont proportionnels à ceux du groupe localement compact ambiant. On peut donc utiliser des théories puissantes concernant certaines classes de groupes localement compacts pour obtenir des calculs des nombres L2 de Betti de leurs réseaux, en particulier les réseaux arithmétiques et les réseaux de Kac–Moody.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.05.013
Petersen, Henrik Densing 1

1 SB-MATHGEOM-EGG, EPFL, Station 8, CH-1015, Lausanne, Switzerland
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Petersen, Henrik Densing. $ {L}^{2}$-Betti numbers of locally compact groups. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 339-342. doi : 10.1016/j.crma.2013.05.013. http://www.numdam.org/articles/10.1016/j.crma.2013.05.013/

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