{"title":"具有Baas-Sullivan奇点流形的指标理论","authors":"R. Deeley","doi":"10.4171/JNCG/269","DOIUrl":null,"url":null,"abstract":"We study index theory for manifolds with Baas-Sullivan singularities using geometric K-homology with coefficients in a unital C*-algebra. In particular, we define a natural analog of the Baum-Connes assembly map for a torsion-free discrete group in the context of these singular spaces. The cases of singularities modelled on k-points (i.e., z/k-manifolds) and the circle are discussed in detail. In the case of the former, the associated index theorem is related to the Freed-Melrose index theorem; in the case of latter, the index theorem is related to work of Rosenberg.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"26 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Index theory for manifolds with Baas-Sullivan singularities\",\"authors\":\"R. Deeley\",\"doi\":\"10.4171/JNCG/269\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study index theory for manifolds with Baas-Sullivan singularities using geometric K-homology with coefficients in a unital C*-algebra. In particular, we define a natural analog of the Baum-Connes assembly map for a torsion-free discrete group in the context of these singular spaces. The cases of singularities modelled on k-points (i.e., z/k-manifolds) and the circle are discussed in detail. In the case of the former, the associated index theorem is related to the Freed-Melrose index theorem; in the case of latter, the index theorem is related to work of Rosenberg.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/JNCG/269\",\"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: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/JNCG/269","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Index theory for manifolds with Baas-Sullivan singularities
We study index theory for manifolds with Baas-Sullivan singularities using geometric K-homology with coefficients in a unital C*-algebra. In particular, we define a natural analog of the Baum-Connes assembly map for a torsion-free discrete group in the context of these singular spaces. The cases of singularities modelled on k-points (i.e., z/k-manifolds) and the circle are discussed in detail. In the case of the former, the associated index theorem is related to the Freed-Melrose index theorem; in the case of latter, the index theorem is related to work of Rosenberg.