Search Results for ""

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 ...

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

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 ...

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 ...

The least genus of any Seifert surface for a given knot. The unknot is the only knot with genus 0. Usually, one denotes by g(K) the genus of the knot K. The knot genus has ...