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submersion (Definition)

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

$\displaystyle \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.



"submersion" is owned by pbruin.
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See Also: immersion
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Cross-references: fibre bundle, open submanifold, image, open mapping, surjective, tangent spaces, tangent map, point, differential manifolds, differentiable map
There is 1 reference to this entry.

This is version 1 of submersion, born on 2005-08-19.
Object id is 7335, canonical name is Submersion.
Accessed 1573 times total.

Classification:
AMS MSC: 53-00 (Differential geometry :: General reference works )
 57R50 (Manifolds and cell complexes :: Differential topology :: Diffeomorphisms)
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