# submersion

A differentiable map $f\colon X\to Y$ differential manifolds $X$ and $Y$ is called a submersion at a point $x\in X$ if the tangent map

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

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 $f\colon X\to Y$ is an open mapping, and its image is an open submanifold of $Y$.

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

Title submersion Submersion 2013-03-22 15:28:49 2013-03-22 15:28:49 pbruin (1001) pbruin (1001) 4 pbruin (1001) Definition msc 53-00 msc 57R50 Immersion