{"paper":{"title":"Aspherical Lagrangian submanifolds, Audin's conjecture and cyclic dilations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Yin Li","submitted_at":"2023-08-09T17:28:54Z","abstract_excerpt":"Given a closed, oriented Lagrangian submanifold $L$ in a Liouville domain $\\overline{M}$, one can define a Maurer-Cartan element with respect to a certain $L_\\infty$-structure on the string homology $\\widehat{H}_\\ast^{S^1}(\\mathcal{L}L;\\mathbb{R})$, completed with respect to the action filtration. When the first Gutt-Hutchings capacity of $\\overline{M}$ is finite, and $L$ is a $K(\\pi,1)$ space, we show that $L$ bounds a pseudoholomorphic disc of Maslov index 2. This confirms a general form of Audin's conjecture and generalizes the works of Fukaya and Irie in the case of $\\mathbb{C}^n$ to a wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.05086","kind":"arxiv","version":6},"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/2308.05086/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"}