{"paper":{"title":"Legendrian embedded contact homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Julian Chaidez, Luya Wang, Oliver Edtmair, Yuan Yao, Ziwen Zhao","submitted_at":"2023-02-14T18:54:35Z","abstract_excerpt":"We give a construction of embedded contact homology (ECH) for a contact $3$-manifold $Y$ with convex sutured boundary and a pair of Legendrians $\\Lambda_+$ and $\\Lambda_-$ contained in $\\partial Y$ satisfying an exactness condition. The chain complex is generated by certain configurations of closed Reeb orbits of $Y$ and Reeb chords of $\\Lambda_+$ to $\\Lambda_-$. The main ingredients include: a general Legendrian adjunction formula for curves in $\\mathbb{R} \\times Y$ with boundary on $\\mathbb{R} \\times \\Lambda$; a relative writhe bound for curves in contact $3$-manifolds asymptotic to Reeb cho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07259","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.07259/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"}