Ehresmann's lemma

Ehresmann's lemma   (Redirected from Ehresmann's theorem) Jump to navigation Jump to search In mathematics, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping {displaystyle fcolon Mrightarrow N} , where {displaystyle M} and {displaystyle N} are smooth manifolds, is a surjective submersion, and a proper map (in particular, this condition is always satisfied if M is compact), then it is a locally trivial fibration. This is a foundational result in differential topology due to Charles Ehresmann, and has many variants.

See also Thom's first isotopy lemma References Ehresmann, Charles (1951), "Les connexions infinitésimales dans un espace fibré différentiable", Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson et Cie., Paris, pp. 29–55, MR 0042768 Kolář, Ivan; Michor, Peter W.; Slovák, Jan (1993). Natural operations in differential geometry. Berlin: Springer-Verlag. ISBN 3-540-56235-4. MR 1202431. Zbl 0782.53013. Categories: Theorems in differential topology