bundle map

Let $E_{1}\overset{\pi_{1}}{\to}B_{1}$ and $E_{2}\overset{\pi_{2}}{\to}B_{2}$ be fiber bundles for which there is a continuous map $f:B_{1}\to B_{2}$ of base spaces. A bundle map (or bundle morphism) is a commutative square

$\xymatrix{E_{1}\ar[r]^{\hat{f}}\ar[d]_{\pi_{1}}&E_{2}\ar[d]^{\pi_{2}}\\ B_{1}\ar[r]^{f}&B_{2}}$

such that the induced map $E_{1}\to f^{-1}E_{2}$ is a homeomorphism (here $f^{-1}E_{2}$ denotes the pullback of $f$ along the bundle projection $\pi_{2}$ ).

Title	bundle map
Canonical name	BundleMap
Date of creation	2013-03-22 13:07:24
Last modified on	2013-03-22 13:07:24
Owner	RevBobo (4)
Last modified by	RevBobo (4)
Numerical id	5
Author	RevBobo (4)
Entry type	Definition
Classification	msc 55R10
Defines	bundle morphism