DOES THE JONES POLYNOMIAL DETECT THE UNKNOT
By Stephen Bigelow. 2000
48 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3b1cc4f11044f4babba3e2f9cc1fbc1d2f8f0cc9
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In Computational Theory and Mathematics
- O. Y. Viro
- L. Rozansky
- Dror Bar-Natan
- J. Scott Carter
- Vladimir Turaev
- R. Fenn
- Alexander Stoimenow
- Simon Willerton
In Discrete Mathematics and Combinatorics
- Tomotada Ohtsuki
- G. Massuyeau
- Simon Willerton
- J. Scott Carter
- Nathan M. Dunfield
- A. Kricker
- L. Rozansky
- Brian Sanderson
In Geometry and Topology
- Jacob Rasmussen
- L. Rozansky
- G. Massuyeau
- Stavros Garoufalidis
- Tomotada Ohtsuki
- Toshie Takata
- S. K. Hansen
- Simon Willerton
Citations in the corpus
- Problems on invariants of knots and 3-manifolds (2004, background): “See [52] (and [53]) for an approach to find such knots by using representations of braid groups.”