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A Study of topology of the Flip Stiefel Manifolds

2023/08/24 by Samik Basu, Basu, Samik, Safikaa Fathima +3
Computer Science · Mathematics · #55T10 #57S17 Secondary : 57R20 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Primary : 57T15 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2308.12702

openalex publication_date 2023/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A well known quotient of the real Stiefel manifold is the projective Stiefel manifold. We introduce a new family of quotients of the real Stiefel manifold by cyclic group of order 2 whose action is induced by simultaneous pairwise flipping of the coordinates. We obtain a description for their tangent bundles, compute their mod 2 cohomology and compute Stiefel Whitney classes of these manifolds. We use these to give applications to their stable span, parallelizability and equivariant maps, and the associated results in topological combinatorics.

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