Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:fiber nontrivial bundle principal S^1-bundle |
| gptkbp:baseSpace |
2-sphere
|
| gptkbp:category |
gptkb:fiber
principal bundle sphere bundle |
| gptkbp:fibersAre |
circles
|
| gptkbp:fiberSpace |
gptkb:butter
|
| gptkbp:field |
gptkb:topology
differential geometry |
| gptkbp:generalizes |
gptkb:higher_Hopf_fibrations
gptkb:octonionic_Hopf_fibration gptkb:quaternionic_Hopf_fibration |
| gptkbp:hasApplication |
gptkb:theoretical_physics
quantum mechanics |
| gptkbp:homotopyGroup |
π_3(S^2) = Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hopf fibration
|
| gptkbp:introduced |
gptkb:Heinz_Hopf
|
| gptkbp:introducedIn |
1931
|
| gptkbp:isFibrationOf |
gptkb:3-sphere
|
| gptkbp:isPrincipalBundle |
yes
|
| gptkbp:projectionMap |
S^3 → S^2
|
| gptkbp:relatedTo |
quaternions
homotopy theory complex projective line |
| gptkbp:structureGroup |
gptkb:circle_group
|
| gptkbp:totalSpace |
gptkb:3-sphere
|
| gptkbp:visualizes |
linked circles
|
| gptkbp:bfsParent |
gptkb:fiber
|
| gptkbp:bfsLayer |
4
|