Geometric limits of knot complements

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 $\BS^3$.

37 pages

References in corpus (2)

• Tameness of hyperbolic 3-manifolds
• Existence of ruled wrappings in hyperbolic 3-manifolds

Cited by in corpus (5)

• Effective bilipschitz bounds on drilling and filling
• Injectivity radii of hyperbolic integer homology 3-spheres
• Systole et rayon maximal des variétés hyperboliques non compactes
• Constructing knots with specified geometric limits
• Geometric limits of knot complements, II: Graphs determined by their complements