Hyperbolic limits of cantor set complements in the sphere

Let M$M$ be a hyperbolic 3‐manifold with no rank two cusps admitting an embedding in S3$\mathbb {S}^3$. Then, if M$M$ admits an exhaustion by π1$\pi _1$‐injective sub‐manifolds there exists Cantor sets Cn⊆S3$C_n\subseteq \mathbb {S}^3$ such that Nn=S3∖Cn$N_n=\mathbb {S}^3\setminus C_n$ is hyperbolic and Nn→M$N_n\rightarrow M$ geometrically.