Ehresmann's lemma

Ehresmann's lemma (Redirected from Ehresmann's theorem) Vai alla navigazione Vai alla ricerca In matematica, or specifically, in differential topology, Ehresmann's lemma or Ehresmann's fibration theorem states that if a smooth mapping {displaystyle fcolon Mrightarrow N} , dove {stile di visualizzazione M} e {stile di visualizzazione N} are smooth manifolds, is a surjective submersion, and a proper map (in particolare, 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, Carlo (1951), "Les connexions infinitésimales dans un espace fibré différentiable", Colloque de topologie (espaces fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson et Cie., Parigi, pp. 29–55, SIG 0042768 Kolář, Ivan; Michor, Peter W.; Slovák, gen (1993). Natural operations in differential geometry. Berlino: Springer-Verlag. ISBN 3-540-56235-4. SIG 1202431. Zbl 0782.53013. Categorie: Theorems in differential topology