Authors: Blagojević, Pavle 
Karasev, Roman
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The Schwarz genus of the Stiefel manifold
Journal: Topology and its Applications
Volume: 160
Issue: 18
First page: 2340
Last page: 2350
Issue Date: 1-Dec-2013
Rank: M22
ISSN: 0166-8641
DOI: 10.1016/j.topol.2013.07.028
In this paper we compute: the Schwarz genus of the Stiefel manifold Vk(Rn) with respect to the action of the Weyl group Wk:=(Z/2)k⋊Sk, and the Lusternik-Schnirelmann category of the quotient space Vk(Rn)/Wk. Furthermore, these results are used in estimating the number of critically outscribed parallelotopes around a strictly convex body, and Birkhoff-James orthogonal bases of a normed finite dimensional vector space.
Keywords: Inscribing and outscribing | Lusternik-Schnirelmann category | Schwarz genus
Publisher: Elsevier
Project: European Unionʼs Seventh Framework Programme (FP7/2007–2013)/ERC, Grant agreement No. 247029-SDModels
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
ERC Advanced Research, Grant No. 267195 (DISCONV)
Presidentʼs of Russian Federation, grant MD-352.2012.1
Russian government, project 11.G34.31.0053

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