Hyperbolic limits of cantor set complements in the sphere

  title={Hyperbolic limits of cantor set complements in the sphere},
  author={Tommaso Cremaschi and Franco Vargas Pallete},
  journal={Bulletin of the London Mathematical Society},
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. 

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