{"title":"Baum-Connes猜想，非交换poincar<s:1>对偶性，以及自由群的边界","authors":"Heath Emerson","doi":"10.1155/S0161171203209169","DOIUrl":null,"url":null,"abstract":"For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra, we construct a canonical K-homology class. This class induces a Poincare duality map K∗(C(∂Γ)⋊Γ)→K∗","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2425-2445"},"PeriodicalIF":1.0000,"publicationDate":"2004-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203209169","citationCount":"10","resultStr":"{\"title\":\"The Baum-Connes conjecture, noncommutative Poincaré duality,and the boundary of the free group\",\"authors\":\"Heath Emerson\",\"doi\":\"10.1155/S0161171203209169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra, we construct a canonical K-homology class. This class induces a Poincare duality map K∗(C(∂Γ)⋊Γ)→K∗\",\"PeriodicalId\":39893,\"journal\":{\"name\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":\"2003 1\",\"pages\":\"2425-2445\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2004-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/S0161171203209169\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/S0161171203209169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/S0161171203209169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Baum-Connes conjecture, noncommutative Poincaré duality,and the boundary of the free group
For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra, we construct a canonical K-homology class. This class induces a Poincare duality map K∗(C(∂Γ)⋊Γ)→K∗
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The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.
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