{"paper":{"title":"Manifolds associated with $(Z_2)^n$-colored regular graphs","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Zhi L\\\"u, Zhiqiang Bao","submitted_at":"2006-09-20T13:40:08Z","abstract_excerpt":"In this article we describe a canonical way to expand a certain kind of $(\\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\\mathbb Z_2)^{n+1}$-manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609557","kind":"arxiv","version":4},"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"}