{"paper":{"title":"How to make a triangulation of S^3 polytopal","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Simon A. King","submitted_at":"2000-09-25T10:03:56Z","abstract_excerpt":"We introduce a numerical isomorphism invariant p(T) for any triangulation T of S^3. Although its definition is purely topological (inspired by the bridge number of knots), p(T) reflects the geometric properties of T.\n Specifically, if T is polytopal or shellable then p(T) is `small' in the sense that we obtain a linear upper bound for p(T) in the number n=n(T) of tetrahedra of T.\n Conversely, if p(T) is `small' then T is `almost' polytopal, since we show how to transform T into a polytopal triangulation by O((p(T))^2) local subdivisions. The minimal number of local subdivisions needed to trans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009216","kind":"arxiv","version":4},"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"}