{"paper":{"title":"Dehn fillings of knot manifolds containing essential once-punctured tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Cameron McA. Gordon, Steven Boyer, Xingru Zhang","submitted_at":"2011-09-23T18:26:16Z","abstract_excerpt":"In this paper we study exceptional Dehn fillings on hyperbolic knot manifolds which contain an essential once-punctured torus. Let $M$ be such a knot manifold and let $\\beta$ be the boundary slope of such an essential once-punctured torus. We prove that if Dehn filling $M$ with slope $\\alpha$ produces a Seifert fibred manifold, then $\\Delta(\\alpha,\\beta)\\leq 5$. Furthermore we classify the triples $(M; \\alpha,\\beta)$ when $\\D(\\alpha,\\beta)\\geq 4$. More precisely, when $\\D(\\alpha,\\beta)=5$, then $M$ is the (unique) manifold $Wh(-3/2)$ obtained by Dehn filling one boundary component of the White"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5151","kind":"arxiv","version":3},"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"}