AI 中文总结
本文定义并研究了持续超图与持续单纯复形及其映射的同调临界点，证明了子集关系的交换图，并给出参数配置空间的实例。
AI 中文摘要
本文研究了持续超图和持续单纯复形的同调临界点。借助相对同调群，我们定义了持续超图之间的持续态射以及持续单纯复形之间的持续单纯映射的同调临界点。我们证明了持续超图及其之间持续态射的同调临界点子集关系的若干交换图。我们还证明了持续单纯复形及其之间持续单纯映射的同调临界点子集关系的若干交换图。通过使用参数配置空间，我们给出了参数独立复形作为填充空间，并给出了参数支配超图作为覆盖空间，作为一些例子。
英文摘要
In this paper, we study the homological critical points for persistence hypergraphs and persistence simplicial complexes. With the help of the relative homology groups, we define the homological critical points for persistence morphisms between persistence hypergraphs and persistence simplicial maps between persistence simplicial complexes. We prove some commutative diagrams of subset relations for the homological critical points of persistence hypergraphs as well as persistence morphisms between them. We also prove some commutative diagrams of subset relations for the homological critical points of persistence simplicial complexes as well as persistence simplicial maps between them. As examples, we use the parametric configuration spaces to construct the parametric independence complexes as the space of parametric packings and construct the parametric dominating hypergraphs as the space of parametric coverings.
Comments33 pages
