{"title":"图形及其维托里斯-里普斯复合物具有相同的伪拓扑弱同调类型","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":"{\"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}","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}
Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type
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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