Path-connectedness of the intersection of translates of St(n,H)

2022/01/29 by Nizar El Idrissi, Idrissi, Nizar El, Samir Kabbaj +3
Computer Science · Mathematics · #54D05 #57N20 #Advanced Combinatorial Mathematics #FOS: Mathematics #General Topology (math.GN) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2201.12642

openalex publication_date 2022/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If H is a Hilbert space, the Stiefel manifold St(n,H) is formed by all the independent n-tuples in H. In this article, we contribute to the topological study of Stiefel manifolds by proving a path-connectedness result. We prove that the intersection of translates of St(n,H) is path-connected by polygonal paths under a condition on the codimension of the span of the components of the translating n-tuples. We rely on a lemma that we prove for the occasion.

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