{"paper":{"title":"Minimal Unital Cyclic $C_\\infty$-Algebras and the Real and Rational Homotopy Type of Closed Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"H\\^ong V\\^an L\\^e","submitted_at":"2026-03-01T18:32:23Z","abstract_excerpt":"Using the notion of isotopy modulo $k$, for $k\\in\\mathbb N^+$, we introduce a stratification on the set of minimal $C_\\infty$-algebra enhancements of a finite-dimensional graded commutative algebra $H^*$. We prove that two such enhancements are $C_\\infty$-isotopic if and only if they are isotopic modulo $k$ for every $k\\in\\mathbb N^+$. We define obstruction sets governing the extension of an isotopy modulo $k$ to an isotopy modulo $(k+1)$ and establish their generalized additivity. We prove that if $M$ is a closed $(r-1)$-connected manifold of dimension $n\\leq \\ell(r-1)+2, \\, r\\geq2,\\quad \\ell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.01219","kind":"arxiv","version":3},"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/2603.01219/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"}