{"paper":{"title":"Closed flat affine 3-manifolds are prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Suhyoung Choi","submitted_at":"2014-07-16T11:41:24Z","abstract_excerpt":"An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\\mathbf R}^3)$. Equivalently an affine $3$-manifold is a $3$-manifold with a flat torsion-free affine connection. We show that a closed affine $3$-manifold is either irreducible or is finitely covered by an affine Hopf manifold. A real projective $3$-manifold is a manifold with an atlas of charts to a real projective space ${\\mathbf R} P^3$ with transition maps in the projective transformation group $PGL(4, {\\mathbf R})$. Using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4264","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"}