# knot

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**Knot invariant**— In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some… …82

**Knot group**— In mathematics, a knot is an embedding of a circle into 3 dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,:pi 1(mathbb{R}^3 ackslash K).Two equivalent knots have… …83

**knot theory**— ▪ mathematics in mathematics, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another. Knots may be regarded as formed by interlacing and looping a piece of string in any… …84

**Knot (disambiguation)**— A knot is a fastening or securing of linear material such as rope, by tying or interweaving. Knot may also refer to:In biology* Several species of birds are commonly known as knots, including: ** Red Knot, a wading bird (simply called Knot in… …85

**Knot energy**— In physical knot theory, a knot energy is a functional on the space of all knot conformations. A conformation of a knot is a particular embedding of a circle into three dimensional space. Depending on the needs of the energy function, the space… …86

**Knot (unit)**— For other uses, see Knot (disambiguation). The knot (pronounced not) is a unit of speed equal to one nautical mile (which is defined as 1.852 km) per hour, approximately 1.151 mph.[1] The abbreviation kn is preferred by the… …87

**knot´less**— knot1 «not», noun, verb, knot|ted, knot|ting. –n. 1. a) a fastening made by tying or twining together pieces of one or more ropes, strings, or cords: »a square knot, a slipknot, a knot in a shoelace. b) …88

**Knot polynomial**— In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. HistoryThe first knot polynomial, the Alexander polynomial, was… …89

**Knot (speed)**— The knot is a unit of speed equal to one nautical mile per hour. Its kn abbreviation is preferred by American and Canadian maritime authorities, [ [http://chartmaker.ncd.noaa.gov/mcd/chart1/chart1hr.htm Positions, Distances, Directions, Compass;… …90

**Knot complement**— In mathematics, the knot complement of a tame knot K is the set theoretic complement of the interior of the embedding of a solid torus into the 3 sphere. This solid torus is a thickened neighborhood of K . Note that the knot complement is a… …