{"paper":{"title":"Hyperbolic 3-manifolds with uniform spectral gap for coclosed 1-forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.GT","authors_text":"Amina Abdurrahman, Anshul Adve, Ben Lowe, Jonathan Zung, Vikram Giri","submitted_at":"2024-04-29T18:26:22Z","abstract_excerpt":"We study two quantifications of being a homology sphere for hyperbolic 3-manifolds, one geometric and one topological: the spectral gap for the Laplacian on coclosed 1-forms and the size of the first torsion homology group. We first construct a sequence of closed hyperbolic integer homology spheres with volume tending to infinity and a uniform coclosed 1-form spectral gap. This answers a question asked by Lin--Lipnowski. We also find sequences of hyperbolic rational homology spheres with the same properties that geometrically converge to a tame limit manifold. Moreover, we show that any such s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19039","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/2404.19039/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"}