Kinoshita–Terasaka knot

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]

Kinoshita–Terasaka knot
Crossing no.11
Genus2
Thistlethwaite11n42
Other
prime, prime, slice
The prime Kinoshita–Terasaka knot (11n42) (left) and the prime Conway knot (11n34) (right) showing how they are related by mutation

References
  1. Weisstein, Eric W. "Conway's Knot". mathworld.wolfram.com. Retrieved 2020-05-19.
  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. Chmutov, S.V. (2007). "Mutant Knots" (PDF). people.math.osu.edu. Archived from the original (PDF) on 2020-06-12.
  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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