论文标题
数据点云的形式形式变形和交点同源性
Stratified Formal Deformations and Intersection Homology of Data Point Clouds
论文作者
论文摘要
相交同源性是一种拓扑不变的，它比普通同源物检测到空间中更细的信息。利用经典简单同义理论中的思想，我们在简单复合物上构建了局部组合转换，在该复合物中，相交同源性仍然不变。特别是，我们获得了复合物的分层形式变形和分层刺的概念，从而导致相交同源性计算之前的复合物减少。我们实施了此类转换的算法执行，以及相交同源性的计算，并应用了这些算法来研究与近乎给定（可能是单一奇异空间）相关的点集相关的与点集相关的点集相关的分层棘的相交同源性。
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes under which intersection homology remains invariant. In particular, we obtain the notions of stratified formal deformations and stratified spines of a complex, leading to reductions of complexes prior to computation of intersection homology. We implemented the algorithmic execution of such transformations, as well as the calculation of intersection homology, and apply these algorithms to investigate the intersection homology of stratified spines in Vietoris-Rips type complexes associated to point sets sampled near given, possibly singular, spaces.
