nLab
pullback bundle

Contents

Context

Bundles

Contents

Idea

Given a bundle p:EXp \colon E \to X, and a morphism f:YXf \colon Y \to X, then the pullback bundle f *EYf^\ast E \to Y is (if it exists) simply the pullback of pp along ff, regarded as a bundle over YY.

Universal bundles

Over a paracompact topological space every vector bundle is isomorphic to a pullback bundle of a universal vector bundle over a classifying space. See there for more.

Notions of pullback:

Last revised on December 2, 2020 at 12:30:39. See the history of this page for a list of all contributions to it.