{"paper":{"title":"Differential forms, Fukaya $A_\\infty$ algebras, and Gromov-Witten axioms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.SG","authors_text":"Jake P. Solomon, Sara B. Tukachinsky","submitted_at":"2016-08-03T19:52:29Z","abstract_excerpt":"Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \\subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\\infty$ structures on $A^*(L),$ parameterized by the cohomology of $X$ relative to $L.$ The family of $A_\\infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_\\infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01304","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/1608.01304/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"}