Comptes Rendus
no. 4
Group Theory
On the set of covolumes of lattices for Fuchsian buildings

Presented by: Étienne Ghys

Anne Thomas1
1 Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 215-218.

We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a Fuchsian building. We use complexes of groups and basic facts about spherical buildings. A consequence is that the set of covolumes of lattices for this building is nondiscrete.

Nous construisons un réseau noncocompact et une famille infinie de réseaux cocompacts dans le groupe d'automorphismes d'un immeuble fuchsien. Nous utilisons des complexes de groupes et quelques propriétés élémentaires des immeubles sphériques. Une conséquence est que l'ensemble des covolumes des réseaux pour cet immeuble est nondiscret.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.12.009

Anne Thomas 1

1 Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA 
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Anne Thomas. On the set of covolumes of lattices for Fuchsian buildings. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 215-218. doi : 10.1016/j.crma.2006.12.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.009/

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[8] J.-P. Serre Cohomologie des groupes discrets, Ann. of Math. Stud., vol. 70, Princeton Univ. Press, Princeton, 1971, pp. 77-169

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