{"paper":{"title":"$S^2$-bundles over 2-orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonathan A. Hillman","submitted_at":"2010-08-25T01:58:25Z","abstract_excerpt":"Let $M$ be a closed 4-manifold with $\\pi_2(M)\\cong{Z}$. Then $M$ is homotopy equivalent to either $CP^2$, or the total space of an orbifold bundle with general fibre $S^2$ over a 2-orbifold $B$, or the total space of an $RP^2$-bundle over an aspherical surface. If $\\pi=\\pi_1(M)\\not=1$ there are at most two such bundle spaces with given action $u:\\pi\\to{Aut}(\\pi_2(M))$. The bundle space has the geometry $\\mathbb{S}^2\\times\\mathbb{E}^2$ (if $\\chi(M)=0$) or $\\mathbb{S}^2\\times\\mathbb{H}^2$ (if $\\chi(M)<0$), except when $B$ is orientable and $\\pi$ is generated by involutions, in which case the act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4186","kind":"arxiv","version":3},"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"}