|
|
|
|
|
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 $\pi_2$ .
|
"bundle map" is owned by RevBobo.
|
|
(view preamble | get metadata)
| Also defines: |
bundle morphism |
|
|
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 4113 times total.
Classification:
| AMS MSC: | 55R10 (Algebraic topology :: Fiber spaces and bundles :: Fiber bundles) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
