Projects per year
Abstract
It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the 3-sphere, then such knots can be taken to lie in the 3-sphere. However, their proof was nonconstructive; no examples were produced. In this paper, we give a constructive proof in the geometrically finite case. That is, given a geometrically finite, tame hyperbolic 3-manifold with one end, we build an explicit family of knots whose complements converge to it geometrically. Our knots lie in the (topological) double of the original manifold. The construction generalises the class of fully augmented links to a Kleinian groups setting.
Original language | English |
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Pages (from-to) | 111-142 |
Number of pages | 32 |
Journal | Pacific Journal of Mathematics |
Volume | 324 |
Issue number | 1 |
DOIs | |
Publication status | Published - 22 Jun 2023 |
Keywords
- circle packing
- fully augmented link
- geometric limit
- Kleinian groups
- knot
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Interactions of geometry and knot theory
Australian Research Council (ARC), Monash University
30/06/17 → 29/06/21
Project: Research