%0 Journal Article
%T The Schwarz genus of the Stiefel manifold and counting geometric configurations
%A Pavle Blagojevi£¿
%A Roman Karasev
%J Mathematics
%D 2012
%I arXiv
%R 10.1016/j.topol.2013.07.028
%X 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.
%U http://arxiv.org/abs/1211.5003v1