{"paper":{"title":"Minimal genus for 4-manifolds with $b^+=1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bo Dai, Chung-I Ho, Tian-Jun Li","submitted_at":"2015-01-01T02:04:46Z","abstract_excerpt":"We derive an adjunction inequality for any smooth, closed, connected, oriented 4-manifold $X$ with $b^+=1$. This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case of $b_1=0$. We demonstrate that the inequality is especially powerful when $2\\tilde \\chi+3\\sigma\\geq 0$, where $\\tilde \\chi$ is the modified Euler number taking account of the cup product on $H^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00235","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"}