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The unknot arises in the mathematical theory of knots. [1]

24 relations: Alexander polynomial, Ambient isotopy, Bight (knot), Circle, Connected sum, Crossing number (knot theory), Cyclic group, Embedding, Finite type invariant, Godfried Toussaint, Homeomorphism, Identity element, Jones polynomial, Knot, Knot (mathematics), Knot complement, Knot group, Knot invariant, Knot theory, Mutation (knot theory), Solid torus, Stuck unknot, Unknotting problem, Unlink.

Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.

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Ambient isotopy

In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an "ambient space", a manifold, taking a submanifold to another submanifold.

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Bight (knot)

In knot tying, a bight is a curved section or slack part between the two ends of a rope, string or yarn.

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A circle is a simple shape in Euclidean geometry.

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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

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Crossing number (knot theory)

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.

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Cyclic group

In algebra, a cyclic group is a group that is generated by a single element.

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In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

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Finite type invariant

In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant, is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities.

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Godfried Toussaint

Godfried T. Toussaint is a Professor of Computer Science and the Head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates.

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In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

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Identity element

In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set.

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Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.

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A knot is a method of fastening or securing linear material such as rope by tying or interweaving.

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Knot (mathematics)

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).

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Knot complement

In mathematics, the knot complement of a tame knot K is the three-dimensional space surrounding the knot.

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Knot group

In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space.

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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.

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Knot theory

In topology, knot theory is the study of mathematical knots.

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Mutation (knot theory)

In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.

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Solid torus

In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle.

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Stuck unknot

In mathematics, a stuck unknot is a closed polygonal chain that is topologically equal to the unknot but cannot be deformed to a simple polygon by rigid motions of the segments.

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Unknotting problem

In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram.

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In the mathematical field of knot theory, the unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane.

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Redirects here:

0 1 knot, 0₁ knot, Standard unknot, Trivial knot.


[1] https://en.wikipedia.org/wiki/Unknot

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