5 papers
Polynomial bounds for surfaces in cusped 3-manifolds
Jessica S. Purcell, Anastasiia Tsvietkova
It is natural to ask how many isotopy classes of embedded essential surfaces lie in a given 3-manifold. The first bounds on the number of such surfaces were exponential, using norm…
Volume bounds for hyperbolic rod complements in the 3-torus
Norman Do, Connie On Yu Hui, Jessica S. Purcell
The study of rod complements is motivated by rod packing structures in crystallography. We view them as complements of links comprised of Euclidean geodesics in the 3-torus. Recent…
Augmented links, shadow links, and the TV volume conjecture: a geometric perspective
Dionne Ibarra, Emma N. McQuire, Jessica S. Purcell
For hyperbolic 3-manifolds, the growth rate of their Turaev-Viro invariants, evaluated at a certain root of unity, is conjectured to give the hyperbolic volume of the manifold. Thi…
Geometry of fully augmented links in doubled 3-manifolds
Jessica S. Purcell, Corbin Reid, John Stewart
Classical fully augmented links have explicit hyperbolic geometry, and have diagrams on the 2-sphere in the 3-sphere. We generalise to construct fully augmented links projected to…
Alternating links on nonorientable surfaces and Klein-bottly alternating links
Jessica S. Purcell, Lecheng Su
It has been known for several decades that classical alternating links in the 3-sphere have nice hyperbolic geometric properties. Recent work generalises such results to give hyper…