22 relations: Alexander polynomial, Chiral knot, Crossing number (knot theory), Fibered knot, Figure-eight knot (mathematics), Hyperbolic link, Hyperbolic volume, Invertible knot, Jones polynomial, Knot theory, Loop (topology), Monic polynomial, Pretzel link, Prime knot, Ribbon knot, Rope, Slice knot, Stevedore knot, Stopper knot, Twist knot, 6₂ knot, 6₃ knot.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image.
In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.
In knot theory, a branch of mathematics, a knot or link K in the 3-dimensional sphere S^3 is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family F_t of Seifert surfaces for K, where the parameter t runs through the points of the unit circle S^1, such that if s is not equal to t then the intersection of F_s and F_t is exactly K. For example.
In knot theory, a figure-eight knot (also called Listing's knot or a Cavendish knot) is the unique knot with a crossing number of four.
In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry.
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric.
In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.
In topology, knot theory is the study of mathematical knots.
A loop in mathematics, in a topological space X is a continuous function f from the unit interval I.
In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.
In the mathematical theory of knots, a pretzel link is a special kind of link.
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.
In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities.
A rope is a group of yarns, plies, fibers or strands that are twisted or braided together into a larger and stronger form.
A slice knot is a type of mathematical knot.
The stevedore knot is a stopper knot, often tied near the end of a rope.
A stopper knot (or simply stopper) is a knot that creates a fixed thicker point on an otherwise uniform thickness rope for the purpose of preventing unreeving: stopping the rope at that point from slipping out of a narrow passage.
In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together.
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot.
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot.