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2020

Verification Of The Jones Unknot Conjecture Up To 24 Crossings

Tuzun, Robert E., Sikora, Adam S.

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Extending upon our previous work, we verify the Jones Unknot Conjecture for all knots up to $24$ crossings.

We describe the method of our approach and analyze the growth of the computational complexity of its different components.

Verification Of The Jones Unknot Conjecture Up To 24 Crossings · Around

Built on

J. H. Conway, An enumeration of knots and links and some of their algebraic properties, In J. Leech (editor), Computational Problems in Abstract Algebra. Oxford, England. Pergamon Press, (1970) 329–358, http://www.maths.ed.ac.uk/~aar/papers/conway.pdf
1970
Earlier work this paper cites.
V.F.R. Jones, Ten problems, in Mathematics: Frontiers and Perspectives (American Mathematical Society Providence, 2000), pp. 79–91
2000
Earlier work this paper cites.

Similar

I. Dynnikov, Arc-presentations of links: monotonic simplification, Fundamenta Mathematicae
2006
Cited alongside, same era.
A. S. Sikora, B. W. Westbury, Confluence Theory for Graphs, Alg. Geom. Topol
2007
Cited alongside, same era.
SnapPy, program for studying the topology and geometry of 3-manifolds, www.math.uic.edu/t3m/SnapPy
Cited in the paper.

Then

S. Ganzell, Local moves and restrictions on the Jones polynomial, J. Knot Theory and its Ramifications
2014
Later among the works it cites.
R. E. Tuzun and A. S. Sikora, Verification of the Jones unknot conjecture to 22 crossings, J. Knot Theory and its Ramifications
2018
Later among the works it cites.

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