BNSR invariants and $\ell^2$-homology
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909068665290752 |
|---|---|
| author | Hughes, Sam Kielak, Dawid |
| author_facet | Hughes, Sam Kielak, Dawid |
| contents | We prove that if the $n$th $\ell^2$-Betti number of a group is non-zero then its $n$th BNSR invariant over $\mathbb{Q}$ is empty, under suitable finiteness conditions. We apply this to answer questions of Friedl--Vidussi and Llosa Isenrich--Py about aspherical Kähler manifolds, to verify some cases of the Singer Conjecture, and to compute certain BNSR invariants of poly-free and poly-surface groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | BNSR invariants and $\ell^2$-homology Hughes, Sam Kielak, Dawid Geometric Topology Algebraic Topology Functional Analysis Group Theory K-Theory and Homology 20J05, 57M07, 20F65, 16S85, 16S35, 57P10, 57N65 We prove that if the $n$th $\ell^2$-Betti number of a group is non-zero then its $n$th BNSR invariant over $\mathbb{Q}$ is empty, under suitable finiteness conditions. We apply this to answer questions of Friedl--Vidussi and Llosa Isenrich--Py about aspherical Kähler manifolds, to verify some cases of the Singer Conjecture, and to compute certain BNSR invariants of poly-free and poly-surface groups. |
| title | BNSR invariants and $\ell^2$-homology |
| topic | Geometric Topology Algebraic Topology Functional Analysis Group Theory K-Theory and Homology 20J05, 57M07, 20F65, 16S85, 16S35, 57P10, 57N65 |
| url | https://arxiv.org/abs/2401.05545 |