Bundle Map - General Morphisms of Fiber Bundles

General Morphisms of Fiber Bundles

Let πE:EM and πF:FN be fiber bundles over spaces M and N respectively. Then a continuous map φ:EF is called a bundle map from E to F if there is a continuous map f:MN such that the diagram

commutes, that is, . In other words, φ is fiber-preserving, and f is the induced map on the space of fibers of E: since πE is surjective, f is uniquely determined by φ. For a given f, such a bundle map φ is said to be a bundle map covering f.

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