{"paper":{"title":"Pre-Calabi-Yau algebras and oriented gravity properad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Sergei Merkulov","submitted_at":"2025-01-19T20:11:32Z","abstract_excerpt":"We study the dual cyclic Hochschild complex $Cyc^\\bullet(A,\\mathbb{K})$ of a (possibly, infinite-dimensional) $A_\\infty$-algebra $(A,\\mu)$ and prove that any pre-Calabi-Yau extension $\\pi$ of the given $A_\\infty$ structure $\\mu$ in $A$ induces on the cyclic cohomology of $(A,\\mu)$ a representation of a new dg properad of oriented ribbon graphs. We compute the cohomology of that properad in terms of the compactly supported cohomology groups of moduli spaces $\\mathcal{M}_{g,m+n}$ of algebraic curves of genus $g$ with $m+n$ marked points.\n  We also show that the gravity operad acts naturally on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11158","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/2501.11158/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"}