pullback bundle

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

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

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.

Last revised on December 27, 2017 at 17:59:42. See the history of this page for a list of all contributions to it.