{"paper":{"title":"Inducing spectral gaps for the cohomological Laplacians of $\\operatorname{Sp}_{2n}(\\mathbb{Z})$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.GR","authors_text":"Jakub Szyma\\'nski, Piotr Mizerka","submitted_at":"2025-04-23T11:31:53Z","abstract_excerpt":"We show that the spectral gap of the first cohomological Laplacian $\\Delta_1$ 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 $n\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16625","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16625/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}