nLab
trivial fiber bundle
Contents
Context
Bundles
bundles

covering space

retractive space

fiber bundle , fiber ∞-bundle

numerable bundle

principal bundle , principal ∞-bundle

associated bundle , associated ∞-bundle

vector bundle , 2-vector bundle , (∞,1)-vector bundle

real , complex /holomorphic , quaternionic

topological , differentiable , algebraic

with connection

bundle of spectra

natural bundle

equivariant bundle

Contents
Idea
The trivial fiber bundle over $B$ with fibre $F$ is simply the Cartesian product $B \times F$ , equipped with the projection map to $B$ to make it a fiber bundle over $B$

$\array{
B \times F
\\
{}^{\mathllap{pr_1}}\downarrow
\\
B
}$

A fiber bundle which not the trivial bundle but is isomorphic to the trivial bundle is called trivializable and the chosen isomorphism is called the corresponding trivialization .

Examples
Last revised on September 13, 2017 at 17:51:32.
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