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Conway's Knot

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Conway's knot is the prime knot on 11 crossings with braid word

sigma_2^3sigma_1sigma_3^(-1)sigma_2^(-2)sigma_1sigma_2^(-1)sigma_1sigma_3^(-1).

The Jones polynomial of Conway's knot is

t^(-4)(-1+2t-2t^2+2t^3+t^6-2t^7+2t^8-2t^9+t^(10)),

which is the same as for the Kinoshita-Terasaka knot.

Conway's knot is not a slice knot (Delbert 2020, Klarreich 2020, Piccirillo 2020).

See also

Kinoshita-Terasaka Knot, Kinoshita-Terasaka Mutants, Knot

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References

Conway, J. H. "An Enumeration of Knots and Links." In Computational Problems in Abstract Algebra (Ed. J. Leech). Oxford, England: Pergamon Press, pp. 329-358, 1970.Cromwell, P. Knots and Links. Cambridge, England: Cambridge University Press, pp. 180-181, 2004.Delbert, C. "Young Mathematician Solves Old, Famous Knot Problem in Barely a Week." Popular Mechanics. May 22, 2020. https://www.popularmechanics.com/science/a32635156/conway-knot-problem-solved/.Klarreich, E. "A Grad Student Solved the Epic Conway Knot Problem--in a Week." Quanta. May 19, 2020. https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/.Montesinos, J. "Surgery on Links and Double Branched Covers of S^3." In Knots, Groups, and 3-Manifolds: Papers dedicated to the memory of R. H. Fox (Ed. L. P. Neuwerth). Princeton, NJ: Princeton University Press, pp. 227-259, 1975.Piccirillo, L. "The Conway Knot Is Not Slice." Ann. Math. 191, 581-591, 2020.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 173, 1976.

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Conway's Knot

Cite this as:

Weisstein, Eric W. "Conway's Knot." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConwaysKnot.html

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