{"title":"On Chen–Yang’s volume conjecture for various quantum invariants","authors":"J. Murakami","doi":"10.4171/IRMA/33-1/9","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/9","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122721007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Triangles on planar Jordan $C^1$-curves and differential topology","authors":"J. Hausmann","doi":"10.4171/IRMA/33-1/2","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/2","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123683698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"What is a black hole? – A geometric introduction","authors":"S. Yamada","doi":"10.4171/IRMA/33-1/26","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/26","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125082887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The paradoxical nature of mathematics","authors":"V. Farmaki, S. Negrepontis","doi":"10.4171/IRMA/33-1/27","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/27","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116492829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"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.
{"title":"Higher holonomy and iterated integrals","authors":"T. Kohno","doi":"10.4171/IRMA/33-1/16","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/16","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":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125554167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dessins for modular operads and the Grothendieck–Teichmüller group","authors":"N. Combe, Y. Manin, M. Marcolli","doi":"10.4171/irma/33-1/24","DOIUrl":"https://doi.org/10.4171/irma/33-1/24","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130087596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On geometric group theory","authors":"V. Poénaru","doi":"10.4171/IRMA/33-1/19","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/19","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128120541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the involution Jimm","authors":"A. M. Uludağ","doi":"10.4171/IRMA/33-1/25","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/25","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130959669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometry of knots and links","authors":"Nikolay A. Abrosimov, A. Mednykh","doi":"10.4171/IRMA/33-1/20","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/20","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127024772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Returns of geometry: From the Pythagoreans to mathematical modernism and beyond","authors":"A. Plotnitsky","doi":"10.4171/IRMA/33-1/28","DOIUrl":"https://doi.org/10.4171/IRMA/33-1/28","url":null,"abstract":"","PeriodicalId":270093,"journal":{"name":"Topology and Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114579709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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