{"paper":{"title":"Toroidal Dehn fillings on hyperbolic 3-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Cameron McA. Gordon, Ying-Qing Wu","submitted_at":"2005-12-01T19:48:30Z","abstract_excerpt":"We determine all hyperbolic 3-manifolds $M$ admitting two toroidal Dehn fillings at distance 4 or 5. We show that if $M$ is a hyperbolic 3-manifold with a torus boundary component $T_0$, and $r,s$ are two slopes on $T_0$ with $\\Delta(r,s) = 4$ or 5 such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of 14 specific manifolds $M_i$, or obtained from $M_1, M_2, M_3$ or $M_{14}$ by attaching a solid torus to $\\partial M_i - T_0$. All the manifolds $M_i$ are hyperbolic, and we show that only the first three can be embedded into $S^3$. As a consequence, this leads to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512038","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0512038/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}