The index of certain Stiefel manifolds

TL;DR

This paper calculates the Fadell-Husseini index for Stiefel manifolds under permutation group actions, specifically for elementary Abelian p-groups, leading to generalizations of a classical topological theorem.

Contribution

It provides explicit computations of the Fadell-Husseini index for Stiefel manifolds with permutation group actions, extending previous results to elementary Abelian p-groups.

Findings

Computed the Fadell-Husseini index for Stiefel manifolds under permutation actions.

Established new generalizations of the Kakutani-Yamabe-Yujobo theorem.

Demonstrated the implications of these indices in topological and geometric contexts.

Abstract

This paper computes the Fadell-Husseini index of Stiefel manifolds in the case where the group acts via permutations of the orthogonal vectors. The computations are carried out in the case of elementary Abelian $p$-groups. The results are shown to imply certain generalizations of the Kakutani-Yamabe-Yujobo theorem.