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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.18594 |
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| _version_ | 1866911399512375296 |
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| author | Fisher, Sam P. Sánchez-Peralta, Pablo |
| author_facet | Fisher, Sam P. Sánchez-Peralta, Pablo |
| contents | Let $G$ be a residually poly-$\mathbb Z$ group of finite type. We prove that $G$ admits a poly-$\mathbb Z$ quotient with kernel $N$ satisfying $\mathrm{cd}_{\mathbb Q}(N) < \mathbb{cd}_{\mathbb Q}(G)$ if and only if the top-dimensional $L^2$-Betti number of $G$ vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the top-dimensional $L^2$-Betti number of residually poly-$\mathbb Z$ groups Fisher, Sam P. Sánchez-Peralta, Pablo Group Theory Let $G$ be a residually poly-$\mathbb Z$ group of finite type. We prove that $G$ admits a poly-$\mathbb Z$ quotient with kernel $N$ satisfying $\mathrm{cd}_{\mathbb Q}(N) < \mathbb{cd}_{\mathbb Q}(G)$ if and only if the top-dimensional $L^2$-Betti number of $G$ vanishes. |
| title | On the top-dimensional $L^2$-Betti number of residually poly-$\mathbb Z$ groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2601.18594 |