The index of equidimensional flag manifolds
Samik Basu, Bikramjit Kundu

TL;DR
This paper computes the Fadell-Husseini index for a specific class of flag manifolds with a cyclic group action, extending previous work on Grassmannians and impacting geometric analysis of convex bodies.
Contribution
It provides a complete calculation of the index for equidimensional flag manifolds with cyclic symmetry, offering new insights into their topological and geometric properties.
Findings
Complete calculation of the Fadell-Husseini index for the flag manifold
Extension of previous Grassmannian index computations to flag manifolds
Implications for p-fold orthogonal shadows of convex bodies
Abstract
In this paper, we consider the flag manifold of orthogonal subspaces of equal dimension which carries an action of the cyclic group of order . 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 . These results have geometric consequences for -fold orthogonal shadows of a convex body.
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Taxonomy
TopicsPoint processes and geometric inequalities · Graph theory and applications · Geometric Analysis and Curvature Flows
