L^p coarse Baum-Connes conjecture via C₀ coarse geometry

2023/11/09 by Hang Wang, Wang, Hang, Yanru Wang +5
Mathematics · #46L80 #55U10 #58B34 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2311.05333

openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the L^p coarse Baum-Connes conjecture for p∈ [1,∞) via C₀ coarse structure, which is a refinement of the bounded coarse structure on a metric space. We prove that the C₀ version of the L^p coarse Baum-Connes conjecture holds for a finite-dimensional simplicial complex equipped with a uniform spherical metric. Using this result, we construct an obstruction group for the L^p coarse Baum-Connes conjecture. As an application, we show that the obstruction group vanishes under the assumption of finite asymptotic dimension, thereby providing a new proof of the L^p coarse Baum-Connes conjecture in this case.

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