St（n，H）的平移交集的路连通性
Path-connectedness of the intersection of translates of St(n,H)
摘要：
如果$H$是一个希尔伯特空间，则Stiefel流形$St(n,H)$由$H$中所有独立的$n$ -元组构成.在这篇文章中，我们通过证明一个路径连通性结果，对Stiefel流形的拓扑研究做出了贡献。证明了在平移$n$ -元组的分量的跨距的余维数满足一定条件下，$St(n,H)$的平移交集是由多边形路连通的.我们依赖于一个引理，我们证明的场合。
英文摘要：
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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