Projects per year
Abstract
It is known that any tame hyperbolic 3manifold 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 3sphere, then such knots can be taken to lie in the 3sphere. 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 3manifold 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 

Pages (fromto)  111142 
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


Interactions of geometry and knot theory
Australian Research Council (ARC), Monash University
30/06/17 → 29/06/21
Project: Research