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.
Keywords
Cite
@article{arxiv.2408.06660,
title = {The maximal coarse Baum-Connes conjecture for spaces that admit an A-by-FCE coarse fibration structure},
author = {Liang Guo and Qin Wang and Chen Zhang},
journal= {arXiv preprint arXiv:2408.06660},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:1208.4543