Spectral gap for products and a strong normal subgroup theorem
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915095429251072 |
|---|---|
| author | Bader, Uri Gelander, Tsachik Levit, Arie |
| author_facet | Bader, Uri Gelander, Tsachik Levit, Arie |
| contents | We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a confined subgroup of an irreducible lattice in a higher rank semisimple Lie group is of finite index. This significantly strengthens the classical normal subgroup theorem of Margulis and removes the property (T) assumption from the recent counterpart result of Fraczyk and Gelander. We further show that any confined discrete subgroup of a higher rank semisimple Lie group satisfying a certain irreducibility condition is an irreducible lattice. This implies a variant of the Stuck-Zimmer conjecture under a strong irreducibility assumption of the action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral gap for products and a strong normal subgroup theorem Bader, Uri Gelander, Tsachik Levit, Arie Group Theory Dynamical Systems 20G25 22E40 37A05 37B99 We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a confined subgroup of an irreducible lattice in a higher rank semisimple Lie group is of finite index. This significantly strengthens the classical normal subgroup theorem of Margulis and removes the property (T) assumption from the recent counterpart result of Fraczyk and Gelander. We further show that any confined discrete subgroup of a higher rank semisimple Lie group satisfying a certain irreducibility condition is an irreducible lattice. This implies a variant of the Stuck-Zimmer conjecture under a strong irreducibility assumption of the action. |
| title | Spectral gap for products and a strong normal subgroup theorem |
| topic | Group Theory Dynamical Systems 20G25 22E40 37A05 37B99 |
| url | https://arxiv.org/abs/2411.07033 |