turkmath.org

In this talk we describe a fibration theorem for real analytic maps $f:\mathbb{R}^n\to\mathbb{R}^p$ with arbitrary singularities. Now suppose that $f$ satisfies Thom's property with respect to a Whitney stratification and let $g:\mathbb{R}^n\to\mathbb{R}^k$ be another real analytic map with isolated singularity at the origin in the stratified sense. We give a Le-Greuel type formula which relates the Euler-Poincaré characteristic of the fibres of $f$ and $(f,g)$. When $f$ and $(f,g)$ are isolated complete intersections we construct an integer valued invariant called the curvature integra which gives the Euler characteristic of the fibres.