fundamental group of knot complement
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:canBe |
non-abelian
infinite group |
| gptkbp:definedIn |
fundamental group of the complement of a knot in S^3
|
| gptkbp:describes |
topological properties of knot complement
|
| gptkbp:example |
gptkb:figure-eight_knot_group
gptkb:trefoil_knot_group gptkb:unknot_group |
| gptkbp:heldBy |
invariant of knots
|
| https://www.w3.org/2000/01/rdf-schema#label |
fundamental group of knot complement
|
| gptkbp:notation |
π₁(S³ \\ K)
|
| gptkbp:presentedBy |
can be given by Wirtinger presentation
|
| gptkbp:property |
finitely presented group
abelianization is Z for any knot depends on knot type |
| gptkbp:relatedTo |
knot
|
| gptkbp:studiedIn |
gptkb:topology
knot theory |
| gptkbp:usedIn |
study of 3-manifolds
knot classification |
| gptkbp:usedToDistinguish |
non-equivalent knots
|
| gptkbp:bfsParent |
gptkb:Wirtinger_presentation
|
| gptkbp:bfsLayer |
6
|