{"paper":{"title":"Characteristic rank of vector bundles over Stiefel manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ajay Singh Thakur, Aniruddha C. Naolekar, J\\'ulius Korba\\v{s}","submitted_at":"2012-09-07T16:58:50Z","abstract_excerpt":"The characteristic rank of a vector bundle $\\xi$ over a finite connected $CW$-complex $X$ is by definition the largest integer $k$, $0\\leq k\\leq \\mathrm{dim}(X)$, such that every cohomology class $x\\in H^j(X;\\mathbb Z_2)$, $0\\leq j\\leq k$, is a polynomial in the Stiefel-Whitney classes $w_i(\\xi)$. In this note we compute the characteristic rank of vector bundles over the Stiefel manifold $V_k(\\mathbb F^n)$, $\\mathbb F=\\mathbb R,\\mathbb C,\\mathbb H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1587","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"}