Ehresmann's lemma

In mathematics, Ehresmann's lemma or Ehresmann's fibration theorem states that a smooth mapping $f:M\rightarrow N$ where M and N are smooth manifolds such that

1. f is a surjective submersion, and
2. 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.