{"paper":{"title":"Hyperbolic volume and Heegaard distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Tsuyoshi Kobayashi, Yo'av Rieck","submitted_at":"2008-03-19T04:14:57Z","abstract_excerpt":"We prove (Theorem~1.5) that there exists a constant $\\Lambda > 0$ so that if $M$ is a $(\\mu,d)$-generic complete hyperbolic 3-manifold of volume $\\vol[M] < \\infty$ and $\\Sigma \\subset M$ is a Heegaard surface of genus $g(\\Sigma) > \\Lambda \\vol[M]$, then $d(\\Sigma) \\leq 2$, where $d(\\Sigma)$ denotes the distance of $\\Sigma$ as defined by Hempel.\n  The key for the proof of the main result is Theorem~1.8 which is on independent interest. There we prove that if $M$ is a compact 3-manifold that can be triangulated using at most $t$ tetrahedra (possibly with missing or truncated vertices), and $\\Sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.2751","kind":"arxiv","version":2},"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"}