{"paper":{"title":"L-spaces, taut foliations and fibered hyperbolic two-bridge links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"For rational homology spheres from Dehn surgery on fibered hyperbolic two-bridge links, not being an L-space is equivalent to supporting a coorientable taut foliation.","cross_cats":[],"primary_cat":"math.GT","authors_text":"Diego Santoro","submitted_at":"2023-04-28T15:32:54Z","abstract_excerpt":"We prove that if $M$ is a rational homology sphere that is Dehn surgery on a fibered hyperbolic two-bridge link, then $M$ is not an $L$-space if and only if $M$ supports a coorientable taut foliation. As a corollary we show that if $K'$ is obtained by a non-trivial knot $K$ as result of an operation called two-bridge replacement, then all non-meridional surgeries on $K'$ support coorientable taut foliations. This operation generalises Whitehead doubling and as a particular case we deduce that all non-meridional surgeries on Whitehead doubles of a non-trivial knot support coorientable taut foli"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"If M is a rational homology sphere that is Dehn surgery on a fibered hyperbolic two-bridge link, then M is not an L-space if and only if M supports a coorientable taut foliation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input manifolds arise specifically from Dehn surgery on fibered hyperbolic two-bridge links; the proof uses geometric and Floer-theoretic properties that hold only for this restricted class of links and the resulting surgeries.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves equivalence between not being an L-space and supporting a coorientable taut foliation for Dehn surgeries on fibered hyperbolic two-bridge links, with corollaries for certain knot surgeries.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For rational homology spheres from Dehn surgery on fibered hyperbolic two-bridge links, not being an L-space is equivalent to supporting a coorientable taut foliation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0b8867f363cc7b04509286cfd93c4c53147139eb1154495918a910d6f61460ec"},"source":{"id":"2304.14914","kind":"arxiv","version":2},"verdict":{"id":"64e866c0-6fc2-44b5-9dea-56ca8e7c5da8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T08:50:30.154787Z","strongest_claim":"If M is a rational homology sphere that is Dehn surgery on a fibered hyperbolic two-bridge link, then M is not an L-space if and only if M supports a coorientable taut foliation.","one_line_summary":"Proves equivalence between not being an L-space and supporting a coorientable taut foliation for Dehn surgeries on fibered hyperbolic two-bridge links, with corollaries for certain knot surgeries.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input manifolds arise specifically from Dehn surgery on fibered hyperbolic two-bridge links; the proof uses geometric and Floer-theoretic properties that hold only for this restricted class of links and the resulting surgeries.","pith_extraction_headline":"For rational homology spheres from Dehn surgery on fibered hyperbolic two-bridge links, not being an L-space is equivalent to supporting a coorientable taut foliation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.14914/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"}