{"paper":{"title":"Duality between Lagrangian and Legendrian invariants","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Tobias Ekholm, Yanki Lekili","submitted_at":"2017-01-05T11:52:52Z","abstract_excerpt":"Consider a pair $(X,L)$, of a Weinstein manifold $X$ with an exact Lagrangian submanifold $L$, with ideal contact boundary $(Y,\\Lambda)$, where $Y$ is a contact manifold and $\\Lambda\\subset Y$ is a Legendrian submanifold. We introduce the Chekanov-Eliashberg DG-algebra, $CE^{\\ast}(\\Lambda)$, with coefficients in chains of the based loop space of $\\Lambda$ and study its relation to the Floer cohomology $CF^{\\ast}(L)$ of $L$. Using the augmentation induced by $L$, $CE^{\\ast}(\\Lambda)$ can be expressed as the Adams cobar construction $\\Omega$ applied to a Legendrian coalgebra, $LC_{\\ast}(\\Lambda)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01284","kind":"arxiv","version":5},"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/1701.01284/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"}