An axiomatic treatment of Persistent Homology

2024/10/08 by Sergio Tsuyoshi Ura, Ura, Sergio Tsuyoshi, Marco Contessoto +3
Computer Science · Mathematics · #55N20 #55N31 #55N40 #55U99 #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2410.05617

openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of axioms.

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