The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.06660
- arXiv:
- arXiv:2408.06660
- Bibcode:
- 2024arXiv240806660G
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Functional Analysis;
- Mathematics - Operator Algebras;
- 19K56;
- 46L80
- E-Print:
- arXiv admin note: text overlap with arXiv:1208.4543