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Conway's knot is the prime knot on 11 crossings with braid word sigma_2^3sigma_1sigma_3^(-1)sigma_2^(-2)sigma_1sigma_2^(-1)sigma_1sigma_3^(-1). The Jones polynomial of ...

The stevedore's knot is the 6-crossing prime knot 6_1. It is implemented in the Wolfram Language as KnotData["Stevedore"]. It has braid word ...

A knot used to join the ends of two ropes together to form a longer length.

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...

A knot is called prime if, for any decomposition as a connected sum, one of the factors is unknotted (Livingston 1993, pp. 5 and 78). A knot which is not prime is called a ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

An invertible knot is a knot that can be deformed via an ambient isotopy into itself but with the orientation reversed. A knot that is not invertible is said to be ...

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...

An oriented knot is an oriented link of one component, or equivalently, it is a knot which has been given an orientation. Given an oriented knot K, reversing the orientation ...

A knot diagram is a picture of a projection of a knot onto a plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the ...