Topological complexity of arithmetic locally symmetric spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915767479435264 |
|---|---|
| author | Frączyk, Mikołaj Hurtado, Sebastian Raimbault, Jean |
| author_facet | Frączyk, Mikołaj Hurtado, Sebastian Raimbault, Jean |
| contents | We prove that any arithmetic locally symmetric space is homotopy equivalent to a simplicial complex where the number of simplices is bounded linearly in the volume of the space. This settles a well-known conjecture of Gelander. The main technical ingredient, which is of independent interest, is a strengthened version of the Margulis' collar lemma for arithmetic locally symmetric spaces based on the height gap theorem of Breuillard, in which the Margulis constant is made linear in the degree of the trace field of the lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_13619 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Topological complexity of arithmetic locally symmetric spaces Frączyk, Mikołaj Hurtado, Sebastian Raimbault, Jean Number Theory Group Theory Geometric Topology 22E40, 11F06, 11F75, 57Q15 We prove that any arithmetic locally symmetric space is homotopy equivalent to a simplicial complex where the number of simplices is bounded linearly in the volume of the space. This settles a well-known conjecture of Gelander. The main technical ingredient, which is of independent interest, is a strengthened version of the Margulis' collar lemma for arithmetic locally symmetric spaces based on the height gap theorem of Breuillard, in which the Margulis constant is made linear in the degree of the trace field of the lattice. |
| title | Topological complexity of arithmetic locally symmetric spaces |
| topic | Number Theory Group Theory Geometric Topology 22E40, 11F06, 11F75, 57Q15 |
| url | https://arxiv.org/abs/2202.13619 |