Geometric limits of knot complements

Jessica S. Purcell; Juan Souto

doi:10.1112/jtopol/jtq020

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arXiv · 0902.1662

Geometric limits of knot complements

Jessica S. Purcell·Juan Souto

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Abstract

We prove that any complete hyperbolic 3--manifold with finitely generated fundamental group, with a single topological end, and which embeds into $\BS^3$ is the geometric limit of a sequence of hyperbolic knot complements in $\BS^3$. In particular, we derive the existence of hyperbolic knot complements which contain balls of arbitrarily large radius. We also show that a complete hyperbolic 3--manifold with two convex cocompact ends cannot be a geometric limit of knot complements in $\BS^3$.

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BibTeX RIS

Jessica S. Purcell, Juan Souto. 2009-02-10. Geometric limits of knot complements. https://doi.org/10.1112/jtopol%2Fjtq020

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