{"paper":{"title":"The Schwarz genus of the Stiefel manifold and counting geometric configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AT","authors_text":"Pavle Blagojevi\\'c, Roman Karasev","submitted_at":"2012-11-21T11:29:10Z","abstract_excerpt":"In this paper we compute: the Schwarz genus of the Stiefel manifold $V_k(\\mathbb R^n)$ with respect to the action of the Weyl group $W_k:=(\\mathbb Z/2)^{k}\\rtimes\\Sigma_k$, and the Lusternik--Schnirelmann category of the quotient space $V_k(\\mathbb R^n)/W_k$. Furthermore, these results are used in estimating the number of: critically outscribed parallelotopes around the strictly convex body, and Birkhoff--James orthogonal bases of the normed finite dimensional vector space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5003","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"}