17. The Fibre Bundle Construction Theorem

In this lecture we discuss morphisms between $G$-fibre bundles, give a recipe for constructing such bundles—the so-called Fibre Bundle Construction Theorem— and show they are determined up to isomorphism by its transition functions.

We conclude by showing how a vector bundle canonically determines a principal bundle via its frame bundle. Next lecture we will investigate the converse direction: producing vector bundles from principal bundles.