Courbures et singularités réelles. (Curvatures and real singularities) (Q1864135)

Summary: Let \(f:\mathbb R^n\rightarrow\mathbb R\) be a polynomial such that \(f(0)=0\) and such that 0 is an isolated critical point of \(f\). Given \(f_t\), a one-parameter smooth deformation of \(f\), we relate the limit: \[ \lim_{\varepsilon \rightarrow 0} \lim_{t \rightarrow 0} \int_{C_t^{\varepsilon}} k dv_t, \] where \(C_t^\varepsilon=f_t^{-1}(0)\cap B_\varepsilon^n\) is the Milnor fiber and \(k\) the curvature, to topological degrees associated with \(f\) and its deformation.