{"paper":{"title":"Smooth manifolds with prescribed rational cohomology ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jim Fowler, Zhixu Su","submitted_at":"2014-03-07T16:44:24Z","abstract_excerpt":"The Hirzebruch signature formula provides an obstruction to the following realization question: given a rational Poincar\\'e duality algebra $\\mathcal{A}$, does there exist a smooth manifold $M$ such that $H^*(M;\\mathbb{Q})=\\mathcal{A}$?\n  This problem is especially interesting for rational truncated polynomial algebras whose corresponding integral algebra is not realizable. For example, there are number theoretic constraints on the dimension $n$ in which there exists a closed smooth manifold $M^n$ with $H^*(M^n;\\mathbb{Q})= \\mathbb{Q}[x]/\\langle x^3\\rangle$. We limit the possible existence dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1801","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"}