The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913655199629312 |
|---|---|
| author | Guo, Liang Wang, Qin Zhang, Chen |
| author_facet | Guo, Liang Wang, Qin Zhang, Chen |
| contents | In this paper, we introduce a concept of A-by-FCE coarse fibration structure for metric spaces, which serves as a generalization of the A-by-CE structure for a sequence of group extensions proposed by Deng, Wang, and Yu. We prove that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry that admit an A-by-FCE coarse fibration structure. As an application, the relative expanders constructed by Arzhantseva and Tessera, as well as the box spaces derived from an ``amenable-by-Haagerup'' group extension, admit the A-by-FCE coarse fibration structure. Consequently, the maximal coarse Baum-Connes conjecture holds for these spaces, which may not admit an FCE structure, i.e. fibred coarse embedding into Hilbert space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure Guo, Liang Wang, Qin Zhang, Chen K-Theory and Homology Functional Analysis Operator Algebras 19K56, 46L80 In this paper, we introduce a concept of A-by-FCE coarse fibration structure for metric spaces, which serves as a generalization of the A-by-CE structure for a sequence of group extensions proposed by Deng, Wang, and Yu. We prove that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry that admit an A-by-FCE coarse fibration structure. As an application, the relative expanders constructed by Arzhantseva and Tessera, as well as the box spaces derived from an ``amenable-by-Haagerup'' group extension, admit the A-by-FCE coarse fibration structure. Consequently, the maximal coarse Baum-Connes conjecture holds for these spaces, which may not admit an FCE structure, i.e. fibred coarse embedding into Hilbert space. |
| title | The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure |
| topic | K-Theory and Homology Functional Analysis Operator Algebras 19K56, 46L80 |
| url | https://arxiv.org/abs/2408.06660 |