To every point in a base space, attach a fibre. The direct product is a trivial bundle.

Examples:

• and , you can get a cylinder or a moebius strip.
• Given manifold M, let . Then E=fiber bundle = TM = =tangent bundle.
• For , is a trivial fibre bundle. Defin projection operator . Then

To relate elements in a fiber on 1 coordinate patch to elements on another patch, demand: . the coefficients of relationship are the structure group. It is for real manifolds.

source psfile jl@crush.caltech.edu index fibre_bundle_equivalence fibre_bundle_section vector_bundle