# submersion

A differentiable map $f:X\to Y$ differential manifolds $X$ and $Y$ is called a *submersion ^{} at a point* $x\in X$ if the tangent map

$$\mathrm{T}f(x):\mathrm{T}X(x)\to \mathrm{T}Y(f(x))$$ |

between the tangent spaces^{} of $X$ and $Y$ at $x$ and $f(x)$ is surjective.

If $f$ is a submersion at every point of $X$, then $f$ is called a *submersion*. A submersion $f:X\to Y$ is an open mapping, and its image is an open submanifold of $Y$.

A fibre bundle $p:X\to B$ over a manifold $B$ is an example of a submersion.

Title | submersion |
---|---|

Canonical name | Submersion |

Date of creation | 2013-03-22 15:28:49 |

Last modified on | 2013-03-22 15:28:49 |

Owner | pbruin (1001) |

Last modified by | pbruin (1001) |

Numerical id | 4 |

Author | pbruin (1001) |

Entry type | Definition |

Classification | msc 53-00 |

Classification | msc 57R50 |

Related topic | Immersion |