The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure

Liang Guo; Qin Wang; Chen Zhang

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arXiv · 2408.06660

The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure

Liang Guo·Qin Wang·Chen Zhang

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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.

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BibTeX RIS

Liang Guo, Qin Wang, Chen Zhang. 2024-08-13. The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure. https://arxiv.org/abs/2408.06660

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