{"title":"Determining homology of an unknown space from a sample","authors":"Morten Brun, Belén García Pascual, Lars M. Salbu","doi":"10.1007/s40879-023-00683-4","DOIUrl":null,"url":null,"abstract":"Abstract The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X , we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40879-023-00683-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a subspace X of Euclidean space and a sample A of points in X , we give conditions for the homology of X to be isomorphic to a certain persistent homology group of the intrinsic Čech complex.
期刊介绍：
The European Journal of Mathematics (EJM) is an international journal that publishes research papers in all fields of mathematics. It also publishes research-survey papers intended to provide nonspecialists with insight into topics of current research in different areas of mathematics. The journal invites authors from all over the world. All contributions are required to meet high standards of quality and originality. EJM has an international editorial board. Coverage in EJM will include: - Algebra - Complex Analysis - Differential Equations - Discrete Mathematics - Functional Analysis - Geometry and Topology - Mathematical Logic and Foundations - Number Theory - Numerical Analysis and Optimization - Probability and Statistics - Real Analysis.
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