论文标题
计算持续的stiefel-whitney类捆绑包
Computing persistent Stiefel-Whitney classes of line bundles
论文作者
论文摘要
我们提出了持续的静态式载体束过滤类的定义。它依赖于将矢量束作为某些欧几里得空间的子集。这种子集的通常的čech过滤可以赋予矢量束结构，我们称为čech束过滤。我们证明这种结构是稳定且一致的。当数据集是线条捆绑包的有限样本时，我们实现了一种有效的算法来计算其持久的stiefel-whitney类。为了在实践中使用简单近似技术，我们提出了一个弱简单近似的概念。作为一个理论上的例子，我们对圆的正常束进行了深入的研究，该研究降低了理解圆环结的持续共同体（1,2）。我们在受图像分析启发的几个数据集上说明了我们的方法。
We propose a definition of persistent Stiefel-Whitney classes of vector bundle filtrations. It relies on seeing vector bundles as subsets of some Euclidean spaces. The usual Čech filtration of such a subset can be endowed with a vector bundle structure, that we call a Čech bundle filtration. We show that this construction is stable and consistent. When the dataset is a finite sample of a line bundle, we implement an effective algorithm to compute its persistent Stiefel-Whitney classes. In order to use simplicial approximation techniques in practice, we develop a notion of weak simplicial approximation. As a theoretical example, we give an in-depth study of the normal bundle of the circle, which reduces to understanding the persistent cohomology of the torus knot (1,2). We illustrate our method on several datasets inspired by image analysis.
