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Loop seen as a trivial knot
Unknot
Common name
Circle
Arf invariant
0
Braid no.
1
Bridge no.
0
Crossing no.
0
Genus
0
Linking no.
0
Stick no.
3
Tunnel no.
0
Unknotting no.
0
Conway notation
-
A–B notation
01
Dowker notation
-
Next
31
Other
torus, fibered, prime, slice, fully amphichiral
Two simple diagrams of the unknot
In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embedded topological circle in the 3-sphere that is ambient isotopic (that is, deformable) to a geometrically round circle, the standard unknot.
The unknot is the only knot that is the boundary of an embedded disk, which gives the characterization that only unknots have Seifert genus 0. Similarly, the unknot is the identity element with respect to the knot sum operation.
mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without...
are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional...
polynomial is characterized by taking the value 1 on any diagram of the unknot and satisfies the following skein relation: ( t 1 / 2 − t − 1 / 2 ) V (...
mathematics, a stuck unknot is a closed polygonal chain in three-dimensional space (a skew polygon) that is topologically equal to the unknot but cannot be deformed...
distinguishes the trefoil from the unknot. The simplest such invariant is tricolorability: the trefoil is tricolorable, but the unknot is not. In addition, virtually...
as well. The standard Möbius strip has the unknot for a boundary but is not a Seifert surface for the unknot because it is not orientable. The "checkerboard"...
Unsolved problem in mathematics: Can unknots be recognized in polynomial time? (more unsolved problems in mathematics) In mathematics, the unknotting...
further negative supercoiling like the latter enzyme. Topoisomerase IV can unknot right-handed knots and decatenate right-handed catenanes without acting...
The Dacre knot, a type of decorative unknot, is a heraldic knot used primarily in English heraldry. It is most notable for its appearance on the Dacre...
the ends together. (That is, a twist knot is any Whitehead double of an unknot.) The twist knots are an infinite family of knots, and are considered the...
first diagram is two unknots with four crossings. Patching the latter P() = A × P() + P() gives, again, a trefoil, and two unknots with two crossings (the...
The unknot is not equivalent to the trefoil knot since one cannot be deformed into the other through a continuous path of homeomorphisms of the ambient...
limited edition BD includes the Tokyo performance of the one-man tour "UNKNOT/REKNOT" held at Zepp DiverCity (Tokyo) on October 15, 2022. At the same...
of components is gcd(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial...
t ) = 1 {\displaystyle {\begin{aligned}P_{n}(unknot)&=q^{n-1}+q^{n-3}+\cdots +q^{1-n}&&n>0\\P_{0}(unknot)&=1\end{aligned}}} For n > 1 {\displaystyle n>1}...
number of Reidemeister moves required to change a diagram of the unknot to the standard unknot. In detail, for any such diagram with c {\displaystyle c} crossings...
links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot - (2,3)-torus knot...
distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial. In...
A heraldic knot (referred to in heraldry as simply a knot) is a knot, unknot, or design incorporating a knot used in European heraldry. While a given knot...
In R 3 {\displaystyle \mathbb {R} ^{3}} , the unknot is not ambient-isotopic to the trefoil knot since one cannot be deformed into the other through a...
property of having the same Alexander polynomial and Conway polynomial as the unknot. The issue of the sliceness of the Conway knot was resolved in 2020 by Lisa...
The Hinckaert knot, a type of decorative unknot, is a heraldic knot used primarily in Dutch heraldry. It is most notable for its appearance on the Hinckaert...
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