{"paper":{"title":"Triangulation, Persistence, and Fukaya categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Jun Zhang, Octav Cornea, Paul Biran","submitted_at":"2023-04-04T13:22:26Z","abstract_excerpt":"This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of morphisms of such a TPC are persistence modules and this category is endowed with a class of weighted distinguished triangles. Under favourable conditions we show that the derived Fukaya category admits a TPC refinement and this is applied to deduce a global rigidity result for spaces of compact, exact Lagrangians in certain Liouville manifolds: we construct "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01785","kind":"arxiv","version":2},"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/2304.01785/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"}