{"paper":{"title":"Unital $C_\\infty$-algebras and the real homotopy type of $(r-1)$-connected compact manifolds of dimension $\\le \\ell(r-1)+2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.DG","math.KT"],"primary_cat":"math.AT","authors_text":"Domenico Fiorenza, H\\^ong V\\^an L\\^e","submitted_at":"2023-10-30T13:04:06Z","abstract_excerpt":"We encode the real homotopy type of an $n$-dimensional $(r-1)$-connected compact manifold $M$, $ r\\ge 2$ into a minimal unital $C_\\infty$-structure on $H^* (M,\\mathbb R)$, obtained via homotopy transfer of the unital DGCA structure of the small quotient algebra associated with a Hodge decomposition of the de Rham algebra $\\mathcal A^*(M)$, which has been proposed by Fiorenza-Kawai-L\\^e-Schwachh\\\"ofer in [Ann. Sc. Norm. Super Pisa (5), vol. XXII (2021), 79-107]. We prove that if $n \\le \\ell (r-1) +2$, with $\\ell \\geq 4$, the multiplication $\\mu_k$ on the minimal unital $C_\\infty$-algebra $H^*(M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.19506","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/2310.19506/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"}