{"paper":{"title":"Volume and Homology for Hyperbolic 3-Orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GT","authors_text":"Peter B. Shalen","submitted_at":"2019-04-24T20:33:47Z","abstract_excerpt":"Let ${\\mathfrak M}$ be a closed, orientable, hyperbolic 3-orbifold such that $\\pi_1({\\mathfrak M})$ contains no hyperbolic triangle group. We show that strict upper bounds of 0.07625, 0.1525 and 0.22875 for ${\\rm vol}\\ {\\mathfrak M}$ imply respective upper bounds of 23, 43 and 79 for $\\dim H_1({\\mathfrak M};{\\mathbb F}_2 )$. Stronger results hold if we assume that the singular set $\\Sigma$ is a link; specifically, under this assumption, strict upper bounds of 0.305, 0.4575, 0.61, 0.7625 and 0.915 for ${\\rm vol}\\ {\\mathfrak M}$ imply respective upper bounds of 7, 13, 14, 28 and 29 for ${\\rm dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11850","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":""},"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"}