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On the Cayley-persistence algebra

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arxiv 2205.10796 v4 pith:OKEWQFH4 submitted 2022-05-22 math.AT

Wanying Bi , Jingyan Li , Jian Liu , Jie Wu This is my paper · ORCID
classification math.AT
keywords cayley-persistencepersistenthomologymoduleintroducepersistence-cupproductstructure
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In this paper, we introduce a persistent (co)homology theory for Cayley digraph grading. We give the algebraic structures of Cayley-persistence object. Specifically, we consider the module structure of persistent (co)homology and show the decomposition of a finitely generated Cayley-persistence module. Moreover, we introduce the persistence-cup product on the Cayley-persistence module and study the twisted structure with respect to the persistence-cup product. As an application on manifolds, we show that the persistent (co)homology is closely related to the persistent map of fundamental classes.

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Cited by 1 Pith paper

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  1. Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review

    math.HO 2025-07 conditional novelty 3.0 of 10

    A survey organizing recent TDA and TDL methods beyond persistent homology and connecting them to data structures and vectorization.

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