Fiber bundles ed

Something that looks locally like a product \[M \times F\] of manifolds.

General ed

definition

Manifolds \[E, M, F\] with (\[M\] base space, \[E\] total space, \[F\] fiber)

a surjective projection \[ \pi : E \rightarrow M \]

\[M\] has a cover of regions \[U \subset M\] with maps \[\psi : \pi^{-1}(U) \rightarrow U \times F\], with \[ \psi(x) = (x,f) \] (local trivialisation)

sections

maps \[ \sigma : M \rightarrow E \] with \[ \pi \circ \sigma = \operatorname{id} \]

Vector bundle ed

Principal fiber bundle ed