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

Abstract

We construct all codimension 1 multi-germs of maps (k^n,T)-->(k^p,0) with n > p-2, (n,p) nice dimensions, k = R or C, by augmentation and concetenation operations, starting from mon-germs (|T|=1). As an application, we prove general results for multi-germs of corank <2: 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 (the comparable result for n>p-1 being already known).