{"title":"Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type","authors":"Jonathan Treviño-Marroquín","doi":"arxiv-2406.00149","DOIUrl":null,"url":null,"abstract":"In this document, we propose a bridge between the graphs and the geometric\nrealizations of their Vietoris Rips complexes, i.e. Graphs, with their\ncanonical \\v{C}ech closure structure, have the same homotopy type that the\nrealization of their Vietoris Rips complex.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"43 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.00149","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this document, we propose a bridge between the graphs and the geometric
realizations of their Vietoris Rips complexes, i.e. Graphs, with their
canonical \v{C}ech closure structure, have the same homotopy type that the
realization of their Vietoris Rips complex.
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