{"paper":{"title":"Combinatorial 2d higher topological quantum field theory from a local cyclic $A_\\infty$ algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AT","math.GT","math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Losev, Justin Beck, Pavel Mnev","submitted_at":"2024-02-06T23:28:01Z","abstract_excerpt":"We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $\\Xi$. In the \"flip theory,\" cells of $\\Xi_\\mathrm{flip}$ correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism $\\Sigma$ a cochain $Z$ on $\\Xi_\\mathrm{flip}$ constructed as a contraction of structure tensors of a cyclic $A_\\infty$ algebra $V$ assigned to polygons. The cyclic $A_\\infty$ equations imply the closedness equation $(\\delta+Q)Z=0$. In this context we define combinatori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.04468","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/2402.04468/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"}