The index of equidimensional flag manifolds

Abstract

In this paper, we consider the flag manifold of $p$ orthogonal subspaces of equal dimension which carries an action of the cyclic group of order $p$. We provide a complete calculation of the associated Fadell-Husseini index. This may be thought of as an odd primary version of the computations of Baralić et al [Forum Math., 30 (2018), pp. 1539--1572] for the Grassmann manifold $G_n({\mathbb{R}}^{2n})$. These results have geometric consequences for $p$-fold orthogonal shadows of a convex body.

23 pages

References in corpus (3)

• Average-Value Tverberg Partitions via Finite Fourier Analysis
• Orthogonal shadows and index of Grassmann manifolds
• The index of certain Stiefel manifolds