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Un théorème de fonctions implicites. Applications

Francis Sergeraert (1973)

Annales de l'institut Fourier

On énonce un théorème de fonctions implicites du type de Nash-Moser, et on indique une application à l’étude des singularités de fonctions différentiables réelles (problème du déploiement universel de Thom).

Unfoldings in Knot Theory.

Walter Neumann, Lee Rudolph (1987)

Mathematische Annalen

Unfoldings Knot Theory (Corrigendum).

Walter Neumann, Lee Rudolph (1988)

Mathematische Annalen

Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

Let $F = (ω)$ be a codim 1 local foliation generated by a germ $ω$ of the form $ω = f_{1} ... f_{p} \sum_{i = 1}^{p} λ_{i} \frac{d f_{i}}{f_{i}}$ for some complex numbers $λ_{i}$ and germs $f_{i}$ of holomorphic functions at the origin in $C^{n}$ . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of $F$ . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for $F$ is equivalent to the unfolding theory for the multiform function...