2024/08/13 by Liang Guo, Qin Wang, Guo, Liang +3 · 1 voice · 1 citation
Mathematics · #19K56 #46L80 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.FA #math.KT #math.OA
paper · pdf · doi:10.48550/arxiv.2408.06660
openalex publication_date 2024/08/13 · arxiv published 2024/08/13 · arxiv updated 2025/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.