{"title":"配置空间与最终预割集上的有向路径","authors":"Jakub Paliga, Krzysztof Ziemia'nski","doi":"10.4064/fm114-9-2021","DOIUrl":null,"url":null,"abstract":"The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the “total” configuration space of points on the plane; by “total” we mean that any finite number of points in a configuration is allowed. We also provide several applications: we define new invariants of precubical sets, prove that directed path spaces on any precubical complex have the homotopy types of CW-complexes and construct certain presentations of configuration spaces of points on the plane as nerves of categories.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Configuration spaces and directed paths\\non the final precubical set\",\"authors\":\"Jakub Paliga, Krzysztof Ziemia'nski\",\"doi\":\"10.4064/fm114-9-2021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the “total” configuration space of points on the plane; by “total” we mean that any finite number of points in a configuration is allowed. We also provide several applications: we define new invariants of precubical sets, prove that directed path spaces on any precubical complex have the homotopy types of CW-complexes and construct certain presentations of configuration spaces of points on the plane as nerves of categories.\",\"PeriodicalId\":55138,\"journal\":{\"name\":\"Fundamenta Mathematicae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-03-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/fm114-9-2021\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/fm114-9-2021","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Configuration spaces and directed paths
on the final precubical set
The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the “total” configuration space of points on the plane; by “total” we mean that any finite number of points in a configuration is allowed. We also provide several applications: we define new invariants of precubical sets, prove that directed path spaces on any precubical complex have the homotopy types of CW-complexes and construct certain presentations of configuration spaces of points on the plane as nerves of categories.
期刊介绍:
FUNDAMENTA MATHEMATICAE concentrates on papers devoted to
Set Theory,
Mathematical Logic and Foundations of Mathematics,
Topology and its Interactions with Algebra,
Dynamical Systems.