42 citations · 434 across the 64 of their papers we have counts for
5 papers · 1 filter
On the tree-width of knot diagrams
Arnaud de Mesmay, Jessica Purcell, Saul Schleimer +1
We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essent…
Treewidth, crushing, and hyperbolic volume
Clément Maria, Jessica S. Purcell
We prove that there exists a universal constant such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most times its volume. The converse is not…
Diagram uniqueness of even plats
Yoav Moriah, Jessica S. Purcell
Every knot has a plat projection, obtained by closing up a braid with bridges. The plat projection is determined by the number of strands and the number of rows of twist regions in…
Geometry of biperiodic alternating links
Abhijit Champanerkar, Ilya Kofman, Jessica S. Purcell
A biperiodic alternating link has an alternating quotient link in the thickened torus. In this paper, we focus on semi-regular links, a class of biperiodic alternating links whose…
Effective distance between nested Margulis tubes
David Futer, Jessica S. Purcell, Saul Schleimer
We give sharp, effective bounds on the distance between tori of fixed injectivity radius inside a Margulis tube in a hyperbolic 3-manifold.