{"paper":{"title":"Nontrivial classes in $H^*(Imb(S^1,\\R^n))$ from nontrivalent graph cocycles","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Riccardo Longoni","submitted_at":"2004-04-09T11:24:32Z","abstract_excerpt":"We construct nontrivial cohomology classes of the space $Imb(S^1,\\R^n)$ of imbeddings of the circle into $\\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\\geq 4$, a de Rham cohomology class on $Imb(S^1,\\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404196","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"}