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Stevedore,s Knot

المؤلف:  Rolfsen, D

المصدر:  Knots and Links. Wilmington, DE: Publish or Perish Press

الجزء والصفحة:  ...

5-6-2021

2885

Stevedore's Knot

The stevedore's knot is the 6-crossing prime knot . It is implemented in the Wolfram Language as KnotData["Stevedore"].

It has braid word . It has Arf invariant 0 and is not amphichiral, although it is invertible. It is a slice knot (Rolfsen 1976, p. 225).

The Alexander polynomial , BLM/Ho polynomial , Conway polynomial , HOMFLY polynomial , and Jones polynomial  of Stevedore's knot are

			(1)
			(2)
			(3)
			(4)
			(5)

Surprisingly, the knot 09-046 shares the same Alexander polynomial with the stevedore's knot. However, no knots on 10 or fewer crossings share the same BLM/Ho polynomial or Jones polynomial with it.

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REFERENCES:

Bar-Natan, D. "The Knot ." https://www.math.toronto.edu/~drorbn/KAtlas/Knots/6.1.html.

KnotPlot. "." https://newweb.cecm.sfu.ca/cgi-bin/KnotPlot/KnotServer/kserver?ncomp=1&ncross=6&id=1.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 225, 1976.