Hyperbolic limits of Cantor set complements in the sphere

Tommaso Cremaschi; Franco Vargas Pallete

Hyperbolic limits of Cantor set complements in the sphere

Geometric Topology 2021-10-12 v2

Authors: Tommaso Cremaschi , Franco Vargas Pallete

Abstract

Let $M$ be a hyperbolic 3-manifold with no rank two cusps admitting an embedding in $\mathbb S^3$ . Then, if $M$ admits an exhaustion by $\pi_1$ -injective sub-manifolds there exists cantor sets $C_n\subset \mathbb S^3$ such that $N_n=\mathbb S^3\setminus C_n$ is hyperbolic and $N_n\rightarrow M$ geometrically.

Keywords

hyperbolic 3-manifold cantor set complement sphere embedding pi1-injective submanifold geometric convergence

Cite

@article{arxiv.2006.03905,
  title  = {Hyperbolic limits of Cantor set complements in the sphere},
  author = {Tommaso Cremaschi and Franco Vargas Pallete},
  journal= {arXiv preprint arXiv:2006.03905},
  year   = {2021}
}

Comments

Version accepted for publication at Bulletin of the London Mathematical Society

Hyperbolic limits of Cantor set complements in the sphere

Abstract

Keywords

Cite

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