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

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.