{"paper":{"title":"Augmentations and immersed Lagrangian fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Dan Rutherford, Yu Pan","submitted_at":"2020-06-29T23:50:29Z","abstract_excerpt":"For a Legendrian link $\\Lambda \\subset J^1M$ with $M = \\mathbb{R}$ or $S^1$, immersed exact Lagrangian fillings $L \\subset \\mbox{Symp}(J^1M) \\cong T^*(\\mathbb{R}_{>0} \\times M)$ of $\\Lambda$ can be lifted to conical Legendrian fillings $\\Sigma \\subset J^1(\\mathbb{R}_{>0} \\times M)$ of $\\Lambda$. When $\\Sigma$ is embedded, using the version of functoriality for Legendrian contact homology (LCH) from [30], for each augmentation $\\alpha: \\mathcal{A}(\\Sigma) \\rightarrow \\mathbb{Z}/2$ of the LCH algebra of $\\Sigma$, there is an induced augmentation $\\epsilon_{(\\Sigma,\\alpha)}: \\mathcal{A}(\\Lambda) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16436","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/2006.16436/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"}