The coarse Baum-Connes conjecture with filtered coefficients and product metric spaces

2024/10/15 by Jianguo Zhang, Zhang, Jianguo · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2410.11662

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the quantitative K-theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There are two advantages for the conjecture with filtered coefficients. Firstly, the routes toward the coarse Baum-Connes conjecture also work for the conjecture with filtered coefficients. Secondly, the class of metric spaces that satisfy the conjecture with filtered coefficients is closed under products and yet it is unknown for the original conjecture. As an application, we discover some new examples of product metric spaces for the coarse Baum-Connes conjecture.

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