Kinoshita–Terasaka_knot

Kinoshita–Terasaka knot

Kinoshita–Terasaka knot

Specific knot in knot theory with 11 crossings

In knot theory, the Kinoshita–Terasaka knot is a particular prime knot. It has 11 crossings.[1] The Kinoshita–Terasaka knot has a variety of interesting mathematical properties.[2] It is related by mutation to the Conway knot,[3] with which it shares a Jones polynomial. It has the same Alexander polynomial as the unknot.[4]

Quick Facts Crossing no., Genus ...
The prime Kinoshita–Terasaka knot (11n42) (left) and the prime Conway knot (11n34) (right) showing how they are related by mutation

References

  1. [1]
    Weisstein, Eric W. "Conway's Knot". mathworld.wolfram.com. Retrieved 2020-05-19.
  2. [2]
    Tillmann, Stephan (June 2000). "On the Kinoshita-Terasaka knot and generalised Conway mutation" (PDF). Journal of Knot Theory and Its Ramifications. 09 (4): 557–575. doi:10.1142/S0218216500000311. ISSN 0218-2165.
  3. [3]
    Chmutov, S.V. (2007). "Mutant Knots" (PDF). people.math.osu.edu. Archived from the original (PDF) on 2020-06-12.
  4. [4]
    Boi, Luciano (2 November 2005). Geometries of Nature, Living Systems and Human Cognition: New Interactions of Mathematics with Natural Sciences and Humanities. ISBN 9789814479455.
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