{"paper":{"title":"Hereditary properties of co-K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AT","authors_text":"Giovanni Bazzoni, Gregory Lupton, John Oprea","submitted_at":"2013-11-22T08:37:54Z","abstract_excerpt":"We show how certain topological properties of co-K{\\\"a}hler manifolds derive from those of the K\\\"ahler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-K\\\"ahler manifolds. As a consequence, we prove that co-K\\\"ahler manifolds satisfy the Toral Rank Conjecture: $\\dim(H^*(M;\\mathbb{Q})) \\geq 2^r$, for any $r$-torus $T^r$ which acts almost freely on $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5675","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"}