{"paper":{"title":"Nonfillable Legendrian knots in the 3-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Tolga Etg\\\"u","submitted_at":"2017-01-27T18:39:29Z","abstract_excerpt":"If a Legendrian knot $\\Lambda$ in the standard contact 3-sphere bounds an orientable exact Lagrangian surface $\\Sigma$ in the standard symplectic 4-ball, then the genus of $\\Sigma$ is equal to the slice genus of (the smooth knot underlying) $\\Lambda$, the sum of the Thurston-Bennequin number of L and the Euler characteristic of $\\Sigma$ is zero as well as the rotation number of $\\Lambda$, and moreover, the linearized contact homology of $\\Lambda$ with respect to the augmentation induced by $\\Sigma$ is isomorphic to the (singular) homology of $\\Sigma$. It was asked in arXiv:1212.1519 whether th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08144","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"}