Geodesic
Géométrie et Topologie, Théorie des groupes
Asymptotic invariants of lattices in locally compact groups
Carderi, Alessandro1 
1 A.C., Institut für Algebra und Geometrie, KIT, 76128 Karlsruhe, Germany
Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 375-415

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The aim of this work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. In particular we will study the asymptotic growth of the Betti numbers of the lattices renormalized by the covolume and the rank gradient, the minimal number of generators also renormalized by the covolume. For doing so we will consider the ultraproduct of the sequence of actions of the locally compact group on the coset spaces and we will show how the properties of one of its cross sections are related to the asymptotic properties of the lattices.

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DOI : 10.5802/crmath.417

Carderi, Alessandro 1

1 A.C., Institut für Algebra und Geometrie, KIT, 76128 Karlsruhe, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Asymptotic invariants of lattices in locally compact groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {375--415},
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Carderi, Alessandro. Asymptotic invariants of lattices in locally compact groups. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 375-415. doi: 10.5802/crmath.417

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