论文标题
对拓扑不变的期望
Expectation of topological invariants
论文作者
论文摘要
在本文中，我们研究了Riemannian歧管上的一组有限的样本点，研究了越野河岩复合物和čech复合物的拓扑不变性值的期望值。我们表明，复合物的Betti数字和Euler特征是比例参数的Lipschitz函数，并且存在一个间隔，以使Betti曲线收敛到基础歧管的Betti数字。
In this paper, we study the expectation values of topological invariants of the Vietoris-Rips complex and Čech complex for a finite set of sample points on a Riemannian manifold. We show that the Betti number and Euler characteristic of the complexes are Lipschitz functions of the scale parameter and that there is an interval such that the Betti curve converges to the Betti number of the underlying manifold.
