nLab
trivial fiber bundle

Context

Bundles

Contents

Idea

The trivial fiber bundle over BB with fibre FF is simply the Cartesian product B×FB \times F, equipped with the projection map to BB to make it a fiber bundle over BB

B×F pr 1 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

Revised on September 13, 2017 13:51:32 by Urs Schreiber (192.41.134.76)