# nLab trivial fiber bundle

### Context

#### Bundles

bundles

fiber bundles in physics

## Context

• dependent type theory

• ## Classes of bundles

• covering space

• numerable bundle

• ## Presentations

• bundle gerbe

• groupal model for universal principal ∞-bundles

• microbundle

• ## Examples

• trivial vector bundle

• tautological line bundle

• basic line bundle on the 2-sphere?
• Hopf fibration

• canonical line bundle

• ## Constructions

• clutching construction

• inner product on vector bundles

• dual vector bundle

• projective 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 13:51:32. See the history of this page for a list of all contributions to it.