# 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.

Title

The Schwarz genus of the Stiefel manifold and counting geometric configurations

Author

Pavle Blagojević, Roman Karasev

Date

2013-12

Source(s)

Appeared in

Topology and its Applications
Volume 160, Issue 18, 1 December 2013, Pages 2335–2339

Type

Text

Size or Duration

7 pages