Related Experiment Video
Updated: Jun 28, 2026

Rotating the Intraocular Lens to Prevent Posterior Capsular Opacification in Cataract Surgeries
Published on: July 7, 2023
Knotted solid tori in contact manifolds
John B Etnyre1, Youlin Li2, Bülent Tosun3
1School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332.
Abstract:
In this paper, we study solid tori in contact manifolds. Specifically, we study the contact width of a knot type and give criteria for when it can be explicitly computed. We also prove there are many "nonthickenable" tori in many knot types. These tori are frequently essential in the study of Legendrian and transverse knot theory and tight contact structures on manifolds obtained by surgery on the knot. Previously, nonthickenable tori have only been observed for iterated torus knots in [Formula: see text] and were thought to be rare. We show that they are quite common, exist in other manifolds, and even for a hyperbolic knot in [Formula: see text]. We also make and highlight several conjectures about the general nature of knots in contact manifolds.
Related Concept Videos
Torsion of Noncircular Members
Toroids
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the...
Torsion in Vector Calculus
Quadric Surfaces
Mohr's Circle for Plane Strain
Mohr's circle visually represents the strain states under various conditions, which is essential for understanding material behavior. The center of Mohr's...
Solid–Solid Solutions
