Ehresmann's theorem

Ehresmann's theorem

In mathematics, Ehresmann's fibration theorem states that a smooth mapping

:"f":"M" → "N"

where "M" and "N" are smooth manifolds, such that

#"f" is a submersion, and
#"f" is a proper map,

is a locally trivial fibration. This is a foundational result in differential topology, and exists in many further variants. It is due to Charles Ehresmann.

References

*Ehresmann, C., "Les connexions infinitésimales dans un espace fibré différentiable", Colloque de Topologie, Bruxelles (1950), 29-55.


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