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Home > 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

  1. f is a submersion, and
  2. 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.

Reference

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

Differential topology

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Ehresmann's Theorem Differential Topology Ehresmann Smooth

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Ehresmann's theoremIn 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  


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