34 relations: Alexander polynomial, Alternating knot, Braid group, Braid theory, Center (group theory), Chirality (mathematics), Cinquefoil knot, Coprime integers, Critical point (mathematics), Crossing number (knot theory), Cylindrical coordinate system, Deformation retract, Dunce hat (topology), Greatest common divisor, Holomorphic function, If and only if, Integer, Irrational winding of a torus, Jones polynomial, Knot (mathematics), Knot group, Knot theory, Link (knot theory), Parametrization, Presentation of a group, Prime knot, Rotational symmetry, Seifert fiber space, Seifert surface, Torus, Trefoil knot, Unknot, 3-sphere, 7₁ knot.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
New!!: Torus knot and Alexander polynomial ·
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link.
New!!: Torus knot and Alternating knot ·
In mathematics, the braid group on strands, denoted by, is a group which has an intuitive geometrical representation, and in a sense generalizes the symmetric group.
New!!: Torus knot and Braid group ·
In topology, a branch of mathematics, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations.
New!!: Torus knot and Braid theory ·
In abstract algebra, the center of a group G, denoted Z(G),The notation Z is from German Zentrum, meaning "center".
New!!: Torus knot and Center (group theory) ·
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot.
New!!: Torus knot and Cinquefoil knot ·
In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled co-prime) if the only positive integer that evenly divides both of them is 1.
New!!: Torus knot and Coprime integers ·
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0 or undefined.
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.
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.
In topology, a branch of mathematics, a retraction is a continuous mapping from the entire space into a subspace which preserves the position of all points in that subspace.
New!!: Torus knot and Deformation retract ·
In topology, the dunce hat is a compact topological space formed by taking a solid triangle and gluing all three sides together, with the orientation of one side reversed.
New!!: Torus knot and Dunce hat (topology) ·
In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder.
In mathematics, holomorphic functions are the central objects of study in complex analysis.
New!!: Torus knot and Holomorphic function ·
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
New!!: Torus knot and If and only if ·
An integer (from the Latin ''integer'' meaning "whole")Integer 's first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: Torus knot and Integer ·
In topology, a branch of mathematics, an irrational winding of a torus is a continuous injection of a line into a torus that is used to set up several counterexamples.
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.
New!!: Torus knot and Jones polynomial ·
In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).
New!!: Torus knot and Knot (mathematics) ·
In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space.
New!!: Torus knot and Knot group ·
In topology, knot theory is the study of mathematical knots.
New!!: Torus knot and Knot theory ·
In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.
New!!: Torus knot and Link (knot theory) ·
Parametrization (or parameterization; also parameterisation, parametrisation) is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model or geometric object.
New!!: Torus knot and Parametrization ·
In mathematics, one method of defining a group is by a presentation.
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.
New!!: Torus knot and Prime knot ·
Generally, an object with 'rotational symmetry' also known in biological contexts as 'radial symmetry', is an object that looks the same after a certain amount of rotation.
New!!: Torus knot and Rotational symmetry ·
A Seifert fiber space is a 3-manifold together with a "nice" decomposition as a disjoint union of circles.
New!!: Torus knot and Seifert fiber space ·
In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is a surface whose boundary is a given knot or link.
New!!: Torus knot and Seifert surface ·
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
New!!: Torus knot and Torus ·
In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.
New!!: Torus knot and Trefoil knot ·
The unknot arises in the mathematical theory of knots.
New!!: Torus knot and Unknot ·
In mathematics, a 3-sphere (also called a glome) is a higher-dimensional analogue of a sphere.
New!!: Torus knot and 3-sphere ·
In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven.
New!!: Torus knot and 7₁ knot ·