持久同调的代数和计算阐述

arXiv - MATH - Algebraic Topology Pub Date : 2024-08-15 DOI:arxiv-2408.07899

Jason Ranoa

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引用次数: 0

摘要

我们从彼得-布贝尼克（Peter Bubenik）、弗雷德里克-查扎尔（FrederikChazal）和乌尔里希-鲍尔（Ulrich Bauer）等作者所采用的持久性模块的现代特征描述角度，讨论了阿夫拉-佐莫罗迪安和贡纳尔-卡尔松在论文《计算持久性同源性》（Computing Persistent Homology）中提出的持久性同源性矩阵还原算法背后的代数。

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An Exposition on the Algebra and Computation of Persistent Homology

We discuss the algebra behind the matrix reduction algorithm for persistent homology, as presented in the paper ''Computing Persistent Homology'' by Afra Zomorodian and Gunnar Carlsson, in the lens of the more modern characterization of persistence modules as functors from a poset category to a category of vector spaces over a field adopted by authors such as Peter Bubenik, Frederik Chazal, and Ulrich Bauer.

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arXiv - MATH - Algebraic Topology

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