{"paper":{"title":"Embedding 3-manifolds with boundary into closed 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dmitry Tonkonog","submitted_at":"2010-03-15T20:56:52Z","abstract_excerpt":"We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere.\n  This is a corollary of the following main result. Let $M$ be a compact connected orientable 3-manifold with boundary. Denote $G=\\Z$, $G=\\Z/p\\Z$ or $G=\\Q$. If $H_1(M;G)\\cong G^k$ and $\\bd M$ is a surface of genus $g$, then the minimal group $H_1(Q;G)$ for closed 3-manifolds $Q$ containing $M$ is isomorphic to $G^{k-g}$.\n  Another corollary is that for a graph $L$ the minimal number $\\rk H_1(Q;\\Z)$ for closed orientable 3-manifolds $Q$ containing $L\\tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3029","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"}