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Kinoshita-Terasaka Knot

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The Kinoshita-Terasaka knot is the prime knot on eleven crossings with braid word

sigma_1^3sigma_3^2sigma_2sigma_3^(-1)sigma_1^(-2)sigma_2sigma_1^(-1)sigma_3^(-1)sigma_2^(-1).

Its Jones polynomial is

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

the same as for Conway's knot. It has the same Alexander polynomial as the unknot.

See also

Conway's Knot, Kinoshita-Terasaka Mutants, Knot, Unknot

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References

Cromwell, P. Knots and Links. Cambridge, England: Cambridge University Press, pp. 98 and 180-181, 2004.Kinoshita, S. and Terasaka, H. "On Unions of Knots." Osaka Math. J. 9, 131-153, 1959.

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Kinoshita-Terasaka Knot

Cite this as:

Weisstein, Eric W. "Kinoshita-Terasaka Knot." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kinoshita-TerasakaKnot.html

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