Global stability for diagrams of differentiable applications

Favaro, Luis Antonio; Mendes, C. M.

Annales de l'Institut Fourier, Tome 36 (1986), p. 133-153 / Harvested from Numdam

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Résumé
Abstract

Dans cet article, nous donnons quelques exemples qui suggèrent la non existence de diagrammes globalement $C^{\infty}$ -stables $R \overset{g}{\leftarrow} M \overset{f}{\to} R$ , $M$ compact. Si $Φ$ : $M \to Q$ est fixe nous définissons la $Φ$ -équivalence pour les applications $f : M \to P$ et la $Φ$ -stabilité correspondante. La procédure de globalisation fonctionne et nous pouvons comparer la $Φ$ -stabilité, la $Φ$ -stabilité infinitésimale et la $Φ$ -stabilité homotopique. Nous donnons aussi quelques théorèmes de caractérisation pour des dimensions inférieures.

In this paper, we give some examples which point to the non-existence of $C^{\infty}$ -global stable diagrams $R \overset{g}{\leftarrow} M \overset{f}{\to} R$ , $M$ compact. If $Φ$ : $M \to Q$ is fixed we define the $Φ$ -equivalence for maps $f : M \to P$ and the corresponding $Φ$ -stability. The globalization procedure works and we can compare the $Φ$ -stability, $Φ$ -infinitesimal stability, and $Φ$ -homotopical stability. Also we give some characterization theorems for lower dimensions.

Publié le : 1986-01-01

MR 87k:58033 | Zbl 0552.58009

DOI : https://doi.org/10.5802/aif.1041

@article{AIF_1986__36_1_133_0,
     author = {Favaro, Luis Antonio and Mendes, C. M.},
     title = {Global stability for diagrams of differentiable applications},
     journal = {Annales de l'Institut Fourier},
     volume = {36},
     year = {1986},
     pages = {133-153},
     doi = {10.5802/aif.1041},
     mrnumber = {87k:58033},
     zbl = {0552.58009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1986__36_1_133_0}
}

Favaro, Luis Antonio; Mendes, C. M. Global stability for diagrams of differentiable applications. Annales de l'Institut Fourier, Tome 36 (1986) pp. 133-153. doi : 10.5802/aif.1041. http://gdmltest.u-ga.fr/item/AIF_1986__36_1_133_0/

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