|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:fiber
gptkb:principal_S^1-bundle
gptkb:nontrivial_bundle
|
|
gptkbp:baseSpace
|
2-sphere
|
|
gptkbp:category
|
gptkb:fiber
gptkb: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
|
|
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:7-dimensional_sphere
gptkb:Differential_Geometry
gptkb:Heinz_Hopf
|
|
gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Hopf fibration
|