math_groups_discgeom

The Schwarz genus of the Stiefel manifold and counting geometric configurations

Pavle Blagojević, Roman Karasev— 2013

Focus Area 3: Topological connectivity and diameter of Discrete Structures 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.

TitelThe Schwarz genus of the Stiefel manifold and counting geometric configurations
VerfasserPavle Blagojević, Roman Karasev
Datum201312
Quelle/n
Erschienen inTopology and its Applications Volume 160, Issue 18, 1 December 2013, Pages 2335–2339
ArtText
Größe oder Länge7 pages