Statements (89)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:canBe |
gptkb:composite_knot
knot |
| gptkbp:classificationProblem |
classify all knots up to ambient isotopy
|
| gptkbp:defines |
embedding of a circle in 3-dimensional Euclidean space
|
| gptkbp:dimensions |
3
|
| gptkbp:example |
gptkb:unknot
gptkb:trefoil_knot figure-eight knot |
| gptkbp:field |
gptkb:topology
knot theory |
| gptkbp:hasApplication |
gptkb:DNA_topology
biology chemistry physics |
| gptkbp:hasCrossingNumber |
minimum number of crossings in a diagram
|
| gptkbp:hasDiagramType |
knot diagram
|
| gptkbp:hasInvariant |
gptkb:Jones_polynomial
gptkb:Alexander_polynomial knot knot genus unknotting number |
| gptkbp:hasProperty |
gptkb:unknot
gptkb:trivial_knot gptkb:Dehn_surgery gptkb:genus gptkb:Conway_polynomial gptkb:Jones_polynomial gptkb:HOMFLY_polynomial gptkb:Seifert_matrix gptkb:Gauss_code gptkb:Alexander_polynomial gptkb:Reidemeister_move gptkb:Dowker_notation gptkb:Seifert_surface gptkb:Montesinos_knot gptkb:composite_knot gptkb:knot_complement knot mutant invertibility cabling chirality satellite operation crossing number tangle alternating knot bridge number fibered knot hyperbolic knot knot sum nonalternating knot planar diagram pretzel knot rational knot ribbon knot satellite knot slice knot colorability nontrivial knot amphichirality arc index arc presentation braid representation bridge index bridge presentation negative knot periodic knot positive knot stick number strongly invertible knot superbridge number tricolorability tunnel number unknotting number |
| gptkbp:hasTable |
Rolfsen knot table
|
| https://www.w3.org/2000/01/rdf-schema#label |
knot (mathematics)
|
| gptkbp:isEquivalentIf |
can be transformed into each other by ambient isotopy
|
| gptkbp:operator |
reversal
mirror image connected sum |
| gptkbp:relatedTo |
gptkb:braid_(mathematics)
link (mathematics) |
| gptkbp:studiedBy |
gptkb:Peter_Guthrie_Tait
Lord Kelvin |
| gptkbp:studiedIn |
knot theory
|
| gptkbp:type |
closed curve
|
| gptkbp:bfsParent |
gptkb:knot
|
| gptkbp:bfsLayer |
5
|