关于持久同调的几何方法

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-03-11 DOI:10.1137/21M1422914

Henry Adams, Baris Coskunuzer

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引用次数: 9

摘要

我们引入了几个几何概念，包括同调类的宽度，来讨论持久同调理论。这些思想提供了持久性图的几何解释。实际上，我们给出了同调类的“寿命”或“持久性”的定量和几何描述。作为案例研究，我们分析了未加权图上的幂过滤，并给出了在所有维度上的持久图中同构类的寿命的显式界限。

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Geometric Approaches on Persistent Homology

We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the"life span"or"persistence"of a homology class. As a case study, we analyze the power filtration on unweighted graphs, and provide explicit bounds for the life spans of homology classes in persistence diagrams in all dimensions.

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