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, for example 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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## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

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## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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## Christmas traditions

Christmas traditions vary from country to country.

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## Circle

A circle is a simple closed shape.

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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 or monogenous group is a group that is generated by a single element.

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## 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.

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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 Canadian Computer Scientist, 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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## 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.

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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, which leaves other elements unchanged when combined with them.

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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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## 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 S^1 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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## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

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## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

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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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## Unlink

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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## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

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## Redirects here:

0 1 knot, 0₁ knot, Culprit unknot, Freedman unknot, Goerlitz unknot, Haken's Gordian unknot, Ligocki-Sethian unknot, Ochiai unknot, Standard unknot, Thistlethwaite knot, Thistlethwaite unknot, Thistlethwaite's unknot, Trivial knot, Twisted Freedman unknot.