Global stability for diagrams of differentiable applications (Q801574)

This paper leads the reader to some difficulties to pass from the local to the global study of stability of divergent diagrams. Some examples are given pointing to the nonexistence of global stable diagrams \(R\leftarrow M\to R\), M compact. Given \(\Phi\) : \(M\to Q\) fixed, the notion of \(\Phi\)- stability for maps \(f: M\to Q\) is introduced as for the corresponding \(\Phi\)-dimensional and \(\Phi\)-homotopical stabilities. The globalization procedure works and some characterization theorems are given for lower dimensions.