Twisted Roe algebras and their $K$-theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916755935330304 |
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| author | Deng, Jintao Guo, Liang |
| author_facet | Deng, Jintao Guo, Liang |
| contents | In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem for metric spaces with a structure of coarse fibrations. We show that the twisted coarse Baum-Connes conjecture with coefficients holds for a metric space with a coarse fibration structure when the base space and the fiber satisfy the twisted coarse Baum-Connes conjecture with coefficients. As an application, the coarse Baum-Connes conjecture holds for a finitely generated group which is an extension of coarsely embeddable groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Roe algebras and their $K$-theory Deng, Jintao Guo, Liang K-Theory and Homology Functional Analysis Operator Algebras 19K56, 47L30 In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem for metric spaces with a structure of coarse fibrations. We show that the twisted coarse Baum-Connes conjecture with coefficients holds for a metric space with a coarse fibration structure when the base space and the fiber satisfy the twisted coarse Baum-Connes conjecture with coefficients. As an application, the coarse Baum-Connes conjecture holds for a finitely generated group which is an extension of coarsely embeddable groups. |
| title | Twisted Roe algebras and their $K$-theory |
| topic | K-Theory and Homology Functional Analysis Operator Algebras 19K56, 47L30 |
| url | https://arxiv.org/abs/2409.16556 |