Does the Jones polynomial detect the unknot?
Stephen J. Bigelow
Abstract
We address the question: Does there exist a non-trivial knot with a trivial Jones polynomial? To find such a knot, it is almost certainly sufficient to find a non-trivial braid on four strands in the kernel of the Burau representation. I will describe a computer algorithm to search for such a braid.
Create a lesson
Related papers
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov
Convex ribbon disks, quasipositivity, and Lagrangian sliceness
Joseph Breen, Alexander Zupan
A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds
Maria Morariu