论文标题
简单和越野撕裂复合物的同位分解
Homotopical decompositions of simplicial and Vietoris Rips complexes
论文作者
论文摘要
在拓扑数据分析中的应用中，我们考虑了由其顶点覆盖引起的简单复合物的分解。我们研究了这种分解的同质类型如何近似简单络合物本身的同质性。通过所谓的阻塞复合物来定量测量简单复合物与这种近似值之间的差异。然后，我们的通用机械专门用于集团复合物，越野杆络合物和公制粘合剂的越野式络合物。对于后者，我们给出的度量条件可以从组件的各个同源物中恢复胶合的第一和零同源性。
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of such decompositions approximates the homotopy of the simplicial complex itself. The difference between the simplicial complex and such an approximation is quantitatively measured by means of the so called obstruction complexes. Our general machinery is then specialized to clique complexes, Vietoris-Rips complexes and Vietoris-Rips complexes of metric gluings. For the latter we give metric conditions which allow to recover the first and zero-th homology of the gluing from the respective homologies of the components.
