{"title":"高完整性和迭代积分","authors":"T. Kohno","doi":"10.4171/IRMA/33-1/16","DOIUrl":null,"url":null,"abstract":"We develop a method to construct representations of the homotopy n-groupoid of a manifold as an n-category by means of K.-T. Chen’s formal homology connections for any positive integer n. We establish a higher holonomy functor from the homotopy n-groupoid to a category obtained from the tensor algebra over the homology of the manifold.","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher holonomy and iterated integrals\",\"authors\":\"T. Kohno\",\"doi\":\"10.4171/IRMA/33-1/16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop a method to construct representations of the homotopy n-groupoid of a manifold as an n-category by means of K.-T. Chen’s formal homology connections for any positive integer n. We establish a higher holonomy functor from the homotopy n-groupoid to a category obtained from the tensor algebra over the homology of the manifold.\",\"PeriodicalId\":270093,\"journal\":{\"name\":\"Topology and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/IRMA/33-1/16\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/IRMA/33-1/16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We develop a method to construct representations of the homotopy n-groupoid of a manifold as an n-category by means of K.-T. Chen’s formal homology connections for any positive integer n. We establish a higher holonomy functor from the homotopy n-groupoid to a category obtained from the tensor algebra over the homology of the manifold.
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