# bundle map

Let ${E}_{1}\stackrel{{\pi}_{1}}{\to}{B}_{1}$ and ${E}_{2}\stackrel{{\pi}_{2}}{\to}{B}_{2}$ 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

$$\text{xymatrix}{E}_{1}\text{ar}{[r]}^{\widehat{f}}\text{ar}{[d]}_{{\pi}_{1}}\mathrm{\&}{E}_{2}\text{ar}{[d]}^{{\pi}_{2}}{B}_{1}\text{ar}{[r]}^{f}\mathrm{\&}{B}_{2}$$ |

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 |