{"paper":{"title":"The defining properties of the Kontsevich unoriented graph complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthemy V. Kiselev, Nina J. Rutten","submitted_at":"2018-11-26T19:00:17Z","abstract_excerpt":"Consider the real vector space of formal sums of non-empty, finite unoriented graphs without multiple edges and loops. Let the vertices of graphs be unlabelled but let every graph $\\gamma$ be endowed with an ordered set of edges $\\mathsf{E}(\\gamma)$. Denote by Gra the vector space of formal sums of graphs modulo the relation $(\\gamma_1,\\mathsf{E}(\\gamma_1))-\\text{sign}(\\sigma) (\\gamma_2,\\mathsf{E}(\\gamma_2)) = 0$ for topologically equal graphs $\\gamma_1$ and $\\gamma_2$ whose edge orderings differ by a permutation $\\sigma$. The zero class in Gra is represented by sums of graphs that cancel via "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10638","kind":"arxiv","version":1},"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"}