{"paper":{"title":"The characteristic rank and cup-length in oriented Grassmann manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"J\\'ulius Korba\\v{s}","submitted_at":"2014-11-25T20:19:14Z","abstract_excerpt":"In the first part, this paper studies the characteristic rank of the canonical oriented $k$-plane bundle over the Grassmann manifold $SO(n)/(SO(k) \\times SO(n-k))$ of oriented $k$-planes in Euclidean $n$-space. It presents infinitely many new exact values if $k = 3$ or $k = 4$, as well as new lower bounds for the number in question if $k > 4$. In the second part, these results enable us to improve on the general upper bounds for the $Z/2Z$-cup-length of $SO(n)/(SO(k) \\times SO(n-k))$. In particular, for $SO(2^t)/(SO(3) \\times SO(2^t-3))$ (with $t > 2$) we prove that the cup-length is equal to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7003","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"}