{"title":"Are two <i>H</i>-Spaces Homotopy Equivalent? An Algorithmic View Point","authors":"Maria Simkova","doi":"10.1142/s1793525323500437","DOIUrl":null,"url":null,"abstract":"This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension $d$. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent.","PeriodicalId":49151,"journal":{"name":"Journal of Topology and Analysis","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793525323500437","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension $d$. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent.
期刊介绍:
This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.