Vanishing topology of codimension 1 multi-germs over $\Bbb R$ and $\Bbb C$

Abstract

We construct all $\cal A$e-codimension 1 multi-germs of analytic (or smooth) maps (kn, T) [rightward arrow] (kp, 0), with n [gt-or-equal, slanted] p − 1, (n, p) nice dimensions, k = $\mathbb C$ or $\mathbb R$, by augmentation and concatenation operations, starting from mono-germs (|T| = 1) and one 0-dimensional bi-germ. As an application, we prove general statements for multi-germs of corank [less-than-or-eq, slant] 1: every one has a real form with real perturbation carrying the vanishing homology of the complexification, every one is quasihomogeneous, and when n = p − 1 every one has image Milnor number equal to 1 (this last is already known when n [gt-or-equal, slanted] p)