The rough Baum–Connes conjecture for uniformly discrete metric spaces

Let $Y$ be a proper and uniformly discrete metric space with coarsely bounded geometry. For each $d\geq 0$, let $P_d(Y)$ be the Rips complex of $Y$, and let $K_*^u(P_d(Y))$ denote its uniform $K$-homology. The uniform coarse assembly map is

$$\mu_u \colon \lim_{d \to \infty} K_*^u(P_d(Y)) \to K_*(C_u^*(Y)).$$

Rough Baum–Connes conjecture. The map $\mu_u$ is an isomorphism. This conjecture asserts that uniform $K$-homology of the Rips complexes computes the $K$-theory of the uniform Roe algebra, extending the coarse Baum–Connes paradigm to the rough setting. The supplied text does not give evidence of a resolution.