Favaro, Mendes: Global stability for diagrams of differentiable applications

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Luis Antonio Favaro; C. M. Mendes
Global stability for diagrams of differentiable applications
Annales de l'institut Fourier, 36 no. 1 (1986), p. 133-153, doi: 10.5802/aif.1041
Article PDF | Reviews MR 87k:58033 | Zbl 0552.58009

Résumé - Abstract

In this paper, we give some examples which point to the non-existence of $C^\infty $-global stable diagrams $R\mathrel {\mathop {\hspace{0.0pt}\leftarrow }\limits ^{g}}M \mathrel {\mathop {\hspace{0.0pt}\rightarrow }\limits ^{f}}R$, $M$ compact. If $\Phi $ : $M\rightarrow Q$ is fixed we define the $\Phi $-equivalence for maps $f: M\rightarrow P$ and the corresponding $\Phi $-stability. The globalization procedure works and we can compare the $\Phi $-stability, $\Phi $-infinitesimal stability, and $\Phi $-homotopical stability. Also we give some characterization theorems for lower dimensions.

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