{"title":"狄拉克-双狄拉克法的下降原理","authors":"Heath Emerson , Ralf Meyer","doi":"10.1016/j.top.2007.02.001","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>G</mi></math></span> be a torsion-free discrete group with a finite-dimensional classifying space <span><math><mi>B</mi><mi>G</mi></math></span>. We show that <span><math><mi>G</mi></math></span> has a dual-Dirac morphism if and only if a certain coarse (co-)assembly map is an isomorphism. Hence the existence of a dual-Dirac morphism for such groups is a metric, that is, coarse, invariant. We get results for groups with torsion as well.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 2","pages":"Pages 185-209"},"PeriodicalIF":0.0000,"publicationDate":"2007-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.02.001","citationCount":"42","resultStr":"{\"title\":\"A descent principle for the Dirac–dual-Dirac method\",\"authors\":\"Heath Emerson , Ralf Meyer\",\"doi\":\"10.1016/j.top.2007.02.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mi>G</mi></math></span> be a torsion-free discrete group with a finite-dimensional classifying space <span><math><mi>B</mi><mi>G</mi></math></span>. We show that <span><math><mi>G</mi></math></span> has a dual-Dirac morphism if and only if a certain coarse (co-)assembly map is an isomorphism. Hence the existence of a dual-Dirac morphism for such groups is a metric, that is, coarse, invariant. We get results for groups with torsion as well.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"46 2\",\"pages\":\"Pages 185-209\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2007.02.001\",\"citationCount\":\"42\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938307000055\",\"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","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938307000055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A descent principle for the Dirac–dual-Dirac method
Let be a torsion-free discrete group with a finite-dimensional classifying space . We show that has a dual-Dirac morphism if and only if a certain coarse (co-)assembly map is an isomorphism. Hence the existence of a dual-Dirac morphism for such groups is a metric, that is, coarse, invariant. We get results for groups with torsion as well.
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