Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
knot |
| gptkbp:AlexanderPolynomial |
(t^{pq}-1)(t-1)/((t^p-1)(t^q-1))
|
| gptkbp:alternating |
false for p,q > 2
|
| gptkbp:appearsIn |
gptkb:algebraic_geometry
gptkb:topology knot theory |
| gptkbp:bridgeType |
min(p,q)
|
| gptkbp:definedIn |
surface of a torus
|
| gptkbp:fibered |
true
|
| gptkbp:genus |
(p-1)(q-1)/2
|
| gptkbp:hasSpecialCase |
unknot if q or p is 1
|
| https://www.w3.org/2000/01/rdf-schema#label |
torus knot T(q,p)
|
| gptkbp:isKnot |
if and only if q and p are coprime
|
| gptkbp:JonesPolynomial |
known formula
|
| gptkbp:mirrorImage |
T(p,q) is mirror of T(q,p)
|
| gptkbp:par |
number of times the knot passes through the hole of the torus
|
| gptkbp:parameter |
integers q and p
|
| gptkbp:primeKnot |
true for p,q > 1
|
| gptkbp:q |
number of times the knot winds around the axis of the torus
|
| gptkbp:symmetry |
cyclic symmetry
|
| gptkbp:bfsParent |
gptkb:knot
|
| gptkbp:bfsLayer |
5
|