Unknot

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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

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.