nLab
trivial fiber bundle
Context
Bundles
bundles

(see also Chern-Weil theory , parameterized homotopy theory )

fiber bundles in physics

Context
slice topos , slice (∞,1)-topos

dependent type theory

Classes of bundles
covering space

fiber bundle , fiber ∞-bundle

numerable bundle

principal bundle , principal ∞-bundle

associated bundle , associated ∞-bundle

vector bundle , (∞,1)-vector bundle

Universal bundles
universal principal bundle , universal principal ∞-bundle

universal vector bundle , universal complex line bundle

subobject classifier , object classifier

Presentations
bundle gerbe

groupal model for universal principal ∞-bundles

microbundle

Examples
trivial vector bundle

tangent bundle , normal bundle

tautological line bundle

basic line bundle on the 2-sphere?
Hopf fibration

canonical line bundle

prequantum circle bundle , prequantum circle n-bundle

Constructions
clutching construction

direct sum of vector bundles , tensor product , external tensor product ,

inner product on vector bundles

dual vector bundle

projective bundle

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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 13:51:32.
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