{"title":"通过归一化循环的简单体积","authors":"C. Loeh, M. Moraschini","doi":"10.1090/proc/15201","DOIUrl":null,"url":null,"abstract":"We show that the Connes-Consani semi-norm on singular homology with real coefficients, defined via s-modules, coincides with the ordinary $\\ell^1$-semi-norm on singular homology in all dimensions.","PeriodicalId":8433,"journal":{"name":"arXiv: Algebraic Topology","volume":"9 2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simplicial volume via normalised cycles\",\"authors\":\"C. Loeh, M. Moraschini\",\"doi\":\"10.1090/proc/15201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the Connes-Consani semi-norm on singular homology with real coefficients, defined via s-modules, coincides with the ordinary $\\\\ell^1$-semi-norm on singular homology in all dimensions.\",\"PeriodicalId\":8433,\"journal\":{\"name\":\"arXiv: Algebraic Topology\",\"volume\":\"9 2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15201\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that the Connes-Consani semi-norm on singular homology with real coefficients, defined via s-modules, coincides with the ordinary $\ell^1$-semi-norm on singular homology in all dimensions.
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