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arXiv · 2207.13302

The index of equidimensional flag manifolds

Samik Basu·Bikramjit Kundu
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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 Barali\'c 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.

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Samik Basu, Bikramjit Kundu. 2022-07-27. The index of equidimensional flag manifolds. https://doi.org/10.1112/mtk.70001

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