DOES THE JONES POLYNOMIAL DETECT THE UNKNOT?

Author:

BIGELOW STEPHEN1

Affiliation:

1. Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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1. Burau Representation of Braid Groups and q-Rationals;International Mathematics Research Notices;2024-01-13

2. An algorithmic method to compute plat slide moves in 3-manifolds of Heegaard genus two;Discrete Mathematics;2023-12

3. Problems, questions, and conjectures about mapping class groups;P SYMP PURE MATH;2019

4. Forks, noodles and the Burau representation for n=4;Transactions of A. Razmadze Mathematical Institute;2018-12

5. Verification of the Jones unknot conjecture up to 22 crossings;Journal of Knot Theory and Its Ramifications;2018-03

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