Bundle Maps
It is useful to have notions of a mapping between two fiber bundles. Suppose that M and N are base spaces, and πE : E → M and πF : F → N are fiber bundles over M and N, respectively. A bundle map (or bundle morphism) consists of a pair of continuous functions
such that . That is, the following diagram commutes:
For fiber bundles with structure group G (such as a principal bundle), bundle morphisms are also required to be G-equivariant on the fibers.
In case the base spaces M and N coincide, then a bundle morphism over M from the fiber bundle πE : E → M to πF : F → M is a map φ : E → F such that . That is, the diagram commutes
A bundle isomorphism is a bundle map which is also a homeomorphism.
Read more about this topic: Fiber Bundle
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