pullback bundle
If is a bundle and is an arbitrary continuous map, then there exists a pullback, or induced, bundle , where
and is the restriction of the projection map to . There is a natural bundle map from to with the map given by , and the map given by the restriction of projection.
If is locally trivial, a principal -bundle, or a fiber bundle, then 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 |