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Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...

Given a doubled knot with the unknot taken as the base knot K_1, the companion knot K_2 of K_1 is called a twist knot with q twists. As illustrated above, the following knots ...

If the knot K is the boundary K=f(S^1) of a singular disk f:D->S^3 which has the property that each self-intersecting component is an arc A subset f(D^2) for which f^(-1)(A) ...

A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

A knot diagram which does not specify whether crossings are under- or overcrossings.

A knot obtained from a tangle which can be represented by a finite sequence of integers.

A knot used to prevent the end of a string from slipping through a hole.

A knot diagram which has alternating under- and overcrossings as the knot projection is traversed. The first knot which does not have an alternating diagram has 8 crossings.

Let R^3 be the space in which a knot K sits. Then the space "around" the knot, i.e., everything but the knot itself, is denoted R^3-K and is called the knot complement of K ...