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6₃ knot

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In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. [1]

14 relations: Alexander polynomial, Alternating knot, Chiral knot, Crossing number (knot theory), Figure-eight knot (mathematics), Hyperbolic link, Hyperbolic volume, Invertible knot, Jones polynomial, Kauffman polynomial, Knot theory, Prime knot, Stevedore knot (mathematics), 6₂ knot.

Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.

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Alternating knot

In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link.

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Chiral knot

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image.

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Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

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Figure-eight knot (mathematics)

In knot theory, a figure-eight knot (also called Listing's knot or a Cavendish knot) is the unique knot with a crossing number of four.

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Hyperbolic link

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry.

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Hyperbolic volume

In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric.

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Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.

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Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.

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Kauffman polynomial

In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman.

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Knot theory

In topology, knot theory is the study of mathematical knots.

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Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.

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Stevedore knot (mathematics)

In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot.

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6₂ knot

In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot.

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References

[1] https://en.wikipedia.org/wiki/6₃_knot

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