{"paper":{"title":"Unobstructed Immersed Lagrangian Correspondence and Filtered $A_{\\infty}$ Functor","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Kenji Fukaya","submitted_at":"2017-06-07T11:14:36Z","abstract_excerpt":"In this paper, we 'construct' a 2-functor from the unobstructed immersed Weinstein category to the category of all filtered $A_{\\infty}$ categories. We consider arbitrary (compact) symplectic manifolds and its arbitrary (relatively spin) immersed Lagrangian submanifolds. The filtered $A_{\\infty}$ category associated to $(X,\\omega)$ is defined by using Lagrangian Floer theory in such generality, see Akaho-Joyce (2010) and Fukaya-Oh-Ohta-Ono (2009). The morphism of unobstructed immersed Weinstein category (from $(X_1,\\omega_1)$ to $(X_2,\\omega_2)$) is by definition a pair of an immersed Lagrangi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02131","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/1706.02131/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"}