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.

TitleThe Schwarz genus of the Stiefel manifold and counting geometric configurations
AuthorPavle Blagojević, Roman Karasev
Date201312
Source(s)
Appeared InTopology and its Applications Volume 160, Issue 18, 1 December 2013, Pages 2335–2339
TypeText
Size or Duration7 pages