unknot
Sign in to saveright|150px|thumb|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.
Key facts
- Knot theory.name
- Unknot
- Knot theory.practical name
- Circle
- Knot theory.image
- Blue Unknot.png
- Knot theory.alt
- The standard unknot.
- Knot theory.arf invariant
- 0
- Knot theory.braid number
- 1
- Knot theory.bridge number
- 0
- Knot theory.crossing number
- 0
- Knot theory.genus
- 0
- Knot theory.linking number
- 0
- Knot theory.stick number
- 3
- Knot theory.unknotting number
- 0
- Knot theory.tunnel number
- 0
- Knot theory.conway_notation
- -
- Knot theory.ab_notation
- 01
- Knot theory.d t_name
- 0a1
- Knot theory.dowker notation
- -
- Knot theory.next crossing
- 3
via Wikipedia infobox
Article
10 sectionsContents
- Background
- Unknotting problem
- Examples
- Hard unknot
- Examples
- Invariants
- Unknotting on a sphere
- See also
- References
- External links
right|150px|thumb|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.