Jessica Purcell - Constructing knots with specified geometric limits - IPAM at UCLA

March 27, 2024
Recorded 27 March 2024. Jessica Purcell of Monash University presents "Constructing knots with specified geometric limits" at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Abstract: Any infinite volume hyperbolic 3-manifold with finitely generated fundamental group that embeds in the 3-sphere is known to be a geometric limit of knot complements, but the original proof was only existential -- no knots were constructed. Using circle packings on the conformal boundaries of tame hyperbolic 3-manifolds, we give a constructive proof of this result -- except we can only guarantee our knots lie in the double of the original manifold, and not in the 3-sphere. Extending to the 3-sphere will require additional properties of circle packings. In this talk, I will discuss the construction and related open questions. This is joint work with Urs Fuchs and John Stewart. Learn more online at: