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View search results from all Wolfram sites (1971 matches)A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...
In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...
A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...
A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...
The Alexander invariant H_*(X^~) of a knot K is the homology of the infinite cyclic cover of the complement of K, considered as a module over Lambda, the ring of integral ...
The arf invariant is a link invariant that always has the value 0 or 1. A knot has Arf invariant 0 if the knot is "pass equivalent" to the unknot and 1 if it is pass ...
A knot which is not a tame knot.
Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...
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 ...
Solomon's seal knot is the prime (5,2)-torus knot 5_1 with braid word sigma_1^5. It is also known as the cinquefoil knot (a name derived from certain herbs and shrubs of the ...
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