KnowraVector bundleLinked fromLinked fromThe 8 pages that link to Vector bundle, each with the reason it gives.All 8Related 3Narrower topic 5Vector fieldNarrower topic: Tangent spaces assemble into a bundle that can host a vector field.Principal symbolRelated: For operators on bundle sections, the principal symbol acts between the corresponding fibers.Characteristic classNarrower topic: Characteristic classes assign cohomological invariants to these families of vector spaces.Atiyah–Singer index theoremRelated: Operators and their symbols often act between bundles over the manifold.Hairy ball theoremNarrower topic: Tangent fields are sections of the sphere's tangent bundle, and the theorem forbids a nonzero section.Michael AtiyahRelated: Vector bundles are central objects in K-theory and many of Atiyah’s geometric investigations.Birkhoff–Grothendieck theoremNarrower topic: The theorem classifies these objects completely when the base is the projective line.Soul theoremNarrower topic: The theorem’s diffeomorphism expresses the manifold as a bundle over its soul.