pullback bundle

If π:EB is a bundle and f:BB is an arbitrary continuous map, then there exists a pullback, or induced, bundle f*(π):EB, where


and f*(π) is the restrictionPlanetmathPlanetmath of the projection map to B. There is a natural bundle mapMathworldPlanetmath from f*(π) to π with the map BB given by f, and the map φ:EE given by the restriction of projection.

If π is locally trivial, a principal G-bundle, or a fiber bundleMathworldPlanetmath, then f*(π) is as well. The pullback satisfies the following universal property:


(i.e. given a diagram with the solid arrows, a map satisfying the dashed arrow exists).

Title pullback bundle
Canonical name PullbackBundle
Date of creation 2013-03-22 13:17:19
Last modified on 2013-03-22 13:17:19
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 7
Author bwebste (988)
Entry type Definition
Classification msc 55R10
Synonym induced bundle