通过测量交叉点的鲁棒性来量化横截性
Quantifying Transversality by Measuring the Robustness of Intersections
摘要：
根据定义，横交在无穷小扰动下是稳定的。使用持久的同源性，我们将这个概念扩展到一个措施。给定一个空间的扰动，我们分配给每个同源类的交集的鲁棒性，在这个空间中的扰动的大小需要杀死它，并证明鲁棒性是稳定的。这一结果的应用是一个稳定的概念的鲁棒性的不动点的连续映射和一个声明的稳定性的轮廓光滑映射。
英文摘要：
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its robustness, the magnitude of a perturbations in this space necessary to kill it, and prove that robustness is stable. Among the applications of this result is a stable notion of robustness for fixed points of continuous mappings and a statement of stability for contours of smooth mappings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
