Milnor's theorem on the total curvature of knots
GPTKB entity
Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
smooth closed curves in R^3
|
| gptkbp:author |
gptkb:John_Milnor
|
| gptkbp:citation |
gptkb:Annals_of_Mathematics,_1950
|
| gptkbp:field |
differential geometry
knot theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Milnor's theorem on the total curvature of knots
|
| gptkbp:implies |
A simple closed curve with total curvature less than 4π is unknotted.
|
| gptkbp:publicationYear |
1950
|
| gptkbp:relatedConcept |
gptkb:Fáry–Milnor_theorem
gptkb:unknot total curvature |
| gptkbp:sentence |
The total curvature of a nontrivial knot in three-dimensional space is at least 4π.
|
| gptkbp:bfsParent |
gptkb:John_W._Milnor
|
| gptkbp:bfsLayer |
4
|