论文标题
组合持续的同源性转换
Combinatorial Persistent Homology Transform
论文作者
论文摘要
最近证明，将持续图作为Möbius倒置的组合解释是函数的。我们采用这一发现来将几何复合物的持续同源转换重塑为$ \ mathbb {s}^n $在组合持续图的类别上的电池的表示。提供了详细的示例。我们希望对pH变换的这种重铸将允许采用从代数和拓扑组合学到形状研究的现有方法。
The combinatorial interpretation of the persistence diagram as a Möbius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a cellulation on $\mathbb{S}^n$ to the category of combinatorial persistence diagrams. Detailed examples are provided. We hope this recasting of the PH transform will allow for the adoption of existing methods from algebraic and topological combinatorics to the study of shapes.
