{"paper":{"title":"Koszul duality patterns in Floer theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.SG","authors_text":"Tolga Etg\\\"u, Yanki Lekili","submitted_at":"2015-02-27T15:08:22Z","abstract_excerpt":"We study symplectic invariants of the open symplectic manifolds $X_\\Gamma$ obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree $\\Gamma$. For any tree $\\Gamma$, we calculate (DG-)algebra models of the Fukaya category $\\mathcal{F}(X_\\Gamma)$ of closed exact Lagrangians in $X_\\Gamma$ and the wrapped Fukaya category $\\mathcal{W}(X_\\Gamma)$. When $\\Gamma$ is a Dynkin tree of type $A_n$ or $D_n$ (and conjecturally also for $E_6,E_7,E_8$), we prove that these models for the Fukaya category $\\mathcal{F}(X_\\Gamma)$ and $\\mathcal{W}(X_\\Gamma)$ are related by (derived) Koszul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07922","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":""},"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"}