Asymptotic invariants of lattices in locally compact groups
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 generato...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.417/ |
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| author | Carderi, Alessandro |
| author_facet | Carderi, Alessandro |
| author_sort | Carderi, Alessandro |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-738853083bb940b3adf279e9f3cc3017 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-738853083bb940b3adf279e9f3cc30172025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G137541510.5802/crmath.41710.5802/crmath.417Asymptotic invariants of lattices in locally compact groupsCarderi, Alessandro0A.C., Institut für Algebra und Geometrie, KIT, 76128 Karlsruhe, GermanyThe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.417/ |
| spellingShingle | Carderi, Alessandro Asymptotic invariants of lattices in locally compact groups Comptes Rendus. Mathématique |
| title | Asymptotic invariants of lattices in locally compact groups |
| title_full | Asymptotic invariants of lattices in locally compact groups |
| title_fullStr | Asymptotic invariants of lattices in locally compact groups |
| title_full_unstemmed | Asymptotic invariants of lattices in locally compact groups |
| title_short | Asymptotic invariants of lattices in locally compact groups |
| title_sort | asymptotic invariants of lattices in locally compact groups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.417/ |
| work_keys_str_mv | AT carderialessandro asymptoticinvariantsoflatticesinlocallycompactgroups |