{"paper":{"title":"Knot contact homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"John Etnyre, Lenhard Ng, Michael Sullivan, Tobias Ekholm","submitted_at":"2011-09-07T19:37:08Z","abstract_excerpt":"The conormal lift of a link $K$ in $\\R^3$ is a Legendrian submanifold $\\Lambda_K$ in the unit cotangent bundle $U^* \\R^3$ of $\\R^3$ with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of $K$, is defined as the Legendrian homology of $\\Lambda_K$, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization $\\R \\times U^*\\R^3$ with Lagrangian boundary condition $\\R \\times \\Lambda_K$.\n  We perform an explicit and complete computation of the Legendrian homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1542","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"}