论文标题
持续同源性终端简单的刚性
Rigidity of terminal simplices in persistent homology
论文作者
论文摘要
给定有限的简单复合物的过滤函数，持续同源性的稳定定理指出，相应的条形码在过滤函数的变化方面是连续的。但是，由于简单复合物的离散设置，关键的简单终止匹配的条不能在过滤功能的任意扰动中不断变化。在本文中，我们提供了足够的条件，即终端单纯形的刚性，即$ε> 0 $的条件，表明同源类别的终端单纯性或持久同源性的端子通过过滤功能的$ε$ - $ε$ - 均保持恒定。同源类别或尺寸n中的条件n取决于尺寸n和n+1中的条形码。
Given a filtration function on a finite simplicial complex, stability theorem of persistent homology states that the corresponding barcode is continuous with respect to changes in the filtration function. However, due to the discrete setting of simplicial complexes, the critical simplices terminating matched bars cannot change continuously for arbitrary perturbations of filtration functions. In this paper we provide a sufficient condition for rigidity of a terminal simplex, i.e., a condition on $ε> 0$ implying that the terminal simplex of a homology class or a bar in persistent homology remains constant through $ε$-perturbations of filtration function. The condition for a homology class or a bar in dimension n depends on the barcodes in dimensions n and n+1.
