{"paper":{"title":"Volume and Homology for Hyperbolic $3$-Orbifolds, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Peter B. Shalen","submitted_at":"2017-09-21T16:58:40Z","abstract_excerpt":"Let ${\\mathfrak M}$ be a closed, orientable, hyperbolic 3-orbifold whose singular set is a link, and such that $\\pi_1({\\mathfrak M})$ contains no hyperbolic triangle group. We show that if the underlying manifold $|{\\mathfrak M}|$ is irreducible, and $|{\\mathfrak M}|$ is irreducible for every two-sheeted (orbifold) covering $\\widetilde{\\mathfrak M}$ of ${\\mathfrak M}$, and if ${\\rm vol} {\\mathfrak M}\\le1.72$, then $\\dim H_1({\\mathfrak M};{\\mathbb Z}_2)\\le 15$. Furthermore, if ${\\rm vol} {\\mathfrak M}\\le1.22$ then $\\dim H_1({\\mathfrak M};{\\mathbb Z}_2)\\le 11$, and if ${\\rm vol} {\\mathfrak M}\\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07413","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"}