{"paper":{"title":"Derived equivalences of gentle algebras via Fukaya categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.SG","authors_text":"Alexander Polishchuk, Yanki Lekili","submitted_at":"2018-01-19T11:31:21Z","abstract_excerpt":"Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra $A$ we associate a triple $(\\Sigma_A, \\Lambda_A; \\eta_A)$, where $\\Sigma_A$ is an oriented smooth surface with non-empty boundary, $\\Lambda_A$ is a set of stops on $\\partial \\Sigma_A$ and $\\eta_A$ is a line field on $\\Sigma_A$, such that the derived category of perfect dg-modules of $A$ is equivalent to the partially wrapped Fukaya category of $(\\Sigma_A, \\Lambda_A ;\\eta_A)$. Modifying arguments of Johnson and Kawazumi, we classify the orbit decomposition of the action of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06370","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/1801.06370/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"}