Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
knot
|
| gptkbp:alsoKnownAs |
gptkb:unknot
|
| gptkbp:category |
gptkb:mathematics
|
| gptkbp:defines |
a knot that is equivalent to a simple loop (the standard embedding of a circle in 3-dimensional space)
|
| gptkbp:distinctiveFeature |
nontrivial knot
|
| gptkbp:field |
gptkb:topology
knot theory |
| gptkbp:hasCrossingNumber |
0
|
| gptkbp:hasInvariant |
Alexander polynomial is 1
Jones polynomial is 1 knot group is the infinite cyclic group unknotting number is 0 |
| https://www.w3.org/2000/01/rdf-schema#label |
trivial knot
|
| gptkbp:isAmphichiral |
true
|
| gptkbp:isCompositeKnot |
false
|
| gptkbp:isPrimeKnot |
false
|
| gptkbp:isTheOnlyKnotWithCrossingNumber |
0
|
| gptkbp:isTheSimplestKnot |
true
|
| gptkbp:property |
can be untangled without cutting
has no crossings |
| gptkbp:represents |
a simple closed curve in 3D space
|
| gptkbp:bfsParent |
gptkb:unknot
gptkb:knot_(mathematics) |
| gptkbp:bfsLayer |
6
|