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Global stability for diagrams of differentiable applications

Luis Antonio Favaro; C. M. Mendes — 1986

Annales de l'institut Fourier

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.

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