Ehresmann's lemma

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

f:M → N

where M and N are smooth manifolds, such that

f is a surjective submersion, and
f is a proper map, (in particular if M is compact)

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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