Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical knot
Topological object |
| gptkbp:characterizedBy |
Two coprime integers (p, q)
|
| gptkbp:definedIn |
Surface of a torus
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Topology |
| gptkbp:hasMirrorImage |
T(q, p)
|
| gptkbp:hasSpecialCase |
T(2,3) is the trefoil knot
T(2,5) is the cinquefoil knot |
| https://www.w3.org/2000/01/rdf-schema#label |
Torus knot
|
| gptkbp:notation |
T(p, q)
|
| gptkbp:property |
Wraps around the torus p times in one direction and q times in the other
Can be represented as a closed braid Chiral for most (p, q) Has a Seifert surface Has a known Alexander polynomial Has a known Jones polynomial Has a known bridge number Has a known crossing number Has a known genus Is a fibered knot Is a periodic knot Is a satellite knot only if p or q is not coprime Is a special case of a torus link Lies on the surface of a torus Nontrivial if both p and q are greater than 1 Prime knot if p and q are coprime |
| gptkbp:relatedTo |
gptkb:Torus_link
Cinquefoil knot Trefoil knot |
| gptkbp:studiedIn |
gptkb:Knot_theory
|
| gptkbp:bfsParent |
gptkb:Torus
|
| gptkbp:bfsLayer |
6
|