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# Unknot

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

## Alexander polynomial

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

## 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.

## Bight (knot)

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

## Circle

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.

## 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.

## Cyclic group

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

## Embedding

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.

## 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.

## 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.

## Homeomorphism

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.

## 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.

## Jones polynomial

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

## Knot

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).

## Knot complement

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

## Knot group

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

## 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.

## Knot theory

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

## Mutation (knot theory)

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

## Solid torus

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

## 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.

## 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.