Inducing spectral gaps for the cohomological Laplacians of $\operatorname{Sp}_{2n}(\mathbb{Z})$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915255018323968 |
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| author | Mizerka, Piotr Szymański, Jakub |
| author_facet | Mizerka, Piotr Szymański, Jakub |
| contents | We show that the spectral gap of the first cohomological Laplacian $Δ_1$ for $\operatorname{Sp}_{2n}(\mathbb{Z})$ follows once a slightly stronger assumption holds for some $\operatorname{Sp}_{2m}(\mathbb{Z})$, where $n\geq m$. As an application of this result, we provide explicit lower bounds for some quotients of $\operatorname{Sp}_{2n}(\mathbb{Z})$ for any $n\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inducing spectral gaps for the cohomological Laplacians of $\operatorname{Sp}_{2n}(\mathbb{Z})$ Mizerka, Piotr Szymański, Jakub Group Theory Functional Analysis Operator Algebras 20G10 We show that the spectral gap of the first cohomological Laplacian $Δ_1$ for $\operatorname{Sp}_{2n}(\mathbb{Z})$ follows once a slightly stronger assumption holds for some $\operatorname{Sp}_{2m}(\mathbb{Z})$, where $n\geq m$. As an application of this result, we provide explicit lower bounds for some quotients of $\operatorname{Sp}_{2n}(\mathbb{Z})$ for any $n\geq 2$. |
| title | Inducing spectral gaps for the cohomological Laplacians of $\operatorname{Sp}_{2n}(\mathbb{Z})$ |
| topic | Group Theory Functional Analysis Operator Algebras 20G10 |
| url | https://arxiv.org/abs/2504.16625 |