{"paper":{"title":"A Note on Closed G_2-Structures and 3-Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.DG","authors_text":"Albert J. Todd, Hyunjoo Cho, Sema Salur","submitted_at":"2011-12-05T04:48:50Z","abstract_excerpt":"This article shows that given any orientable 3-manifold X, the 7-manifold T^*X x R admits a closed G_2-structure varphi=Re(Omega)+omega\\wedge dt where Omega is a certain complex-valued 3-form on T^*X; next, given any 2-dimensional submanifold S of X, the conormal bundle N^*S of S is a 3-dimensional submanifold of T^*X x R such that varphi restricted to N^*S is equivalent to 0. A corollary of the proof of this result is that N^*S x R is a 4-dimensional submanifold of T^*X x R such that varphi restricted to N^*S x R is equivalent to 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0830","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"}