{"paper":{"title":"Supersymmetry and cohomology of graph complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Serguei Barannikov","submitted_at":"2018-03-30T17:39:25Z","abstract_excerpt":"This is preprint HAL-00429963 (2009). I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves $\\widehat{Z}_{I}\\in H^{*}(\\bar{\\mathcal{M}}_{g,n})$ starting from the following data: an odd derivation $I$, whose square is non-zero in general, $I^{2}\\neq 0$, acting on a $\\mathbb{Z}/2\\mathbb{Z}$-graded associative algebra with odd scalar product. The constructed cocycles were first described in the theorem 2 in the author's paper \"Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals\". Comptes Rendus Mathematique, 348, pp. 359-362, arXiv:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11549","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":""},"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"}