Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A fibre bundle is a structure (E, B, π, F) where E is the total space, B is the base space, π: E → B is a continuous surjection, and F is the fibre, such that locally E looks like B × F.
|
| gptkbp:example |
gptkb:Möbius_strip
gptkb:Hopf_fibration gptkb:principal_G-bundle vector bundle line bundle frame bundle cotangent bundle sphere bundle tangent bundle normal bundle trivial bundle nontrivial bundle |
| gptkbp:field |
gptkb:mathematics
gptkb:topology differential geometry |
| gptkbp:generalizes |
covering space
principal bundle vector bundle |
| gptkbp:hasApplication |
gptkb:algebraic_geometry
gptkb:general_relativity gptkb:quantum_field_theory gptkb:K-theory gptkb:string_theory control theory dynamical systems fiber optics mechanics partial differential equations robotics twistor theory homotopy theory index theory complex geometry gauge bosons foliation theory fibered manifold |
| gptkbp:hasInvariant |
gptkb:Chern_class
gptkb:Stiefel–Whitney_class Euler class Pontryagin class characteristic class obstruction theory |
| gptkbp:hasPart |
base space
projection map total space fibre |
| gptkbp:hasProperty |
locally trivial
|
| https://www.w3.org/2000/01/rdf-schema#label |
fibre bundle
|
| gptkbp:introduced |
gptkb:Herbert_Seifert
|
| gptkbp:relatedTo |
gptkb:manga_series
transition function structure group |
| gptkbp:usedIn |
gptkb:gauge_theory
gptkb:theoretical_physics gptkb:topology differential topology |
| gptkbp:bfsParent |
gptkb:The_Topology_of_Fibre_Bundles
|
| gptkbp:bfsLayer |
7
|