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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 $V_k(\\mathbb F^n)$, $\\mathbb F=\\mathbb R,\\mathbb C,\\mathbb H$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.1587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-07T16:58:50Z","cross_cats_sorted":[],"title_canon_sha256":"8e87f56ed3c478fad53a84d931eb9e84c52412781225739a18ab6c1b638992d7","abstract_canon_sha256":"ae77d50800b965872177a2c6536b128d74d188256529fbe5967a01ee082a33ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:13.922211Z","signature_b64":"WegMnNIuw3HFa/eeczhO3WC0OzZZ8qJqc1socj3QWvsg0/ombx4FGfsiaWGhzwopUub38gZ8YNOMFzTzZgBsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"886632939ac70a81384f1e3a8ae9a2800ad58dfda35a072b7550265fea552b98","last_reissued_at":"2026-05-18T03:38:13.921539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:13.921539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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