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bundle map (Definition)

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

$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ E_1 \ar[r]^{\hat{f}} \ar[d]_{\pi_1} & E_2 \ar[d]^{\pi_2} \ B_1 \ar[r]^{f} & B_2 } } \end{xy}$
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$).



"bundle map" is owned by RevBobo.
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Also defines:  bundle morphism
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Cross-references: projection, pullback, homeomorphism, map, induced, square, commutative, base, continuous map, fiber bundles
There are 3 references to this entry.

This is version 2 of bundle map, born on 2002-11-01, modified 2003-08-18.
Object id is 3557, canonical name is BundleMap.
Accessed 3009 times total.

Classification:
AMS MSC55R10 (Algebraic topology :: Fiber spaces and bundles :: Fiber bundles)

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