Abstract
This project is concerned with vanishing homology of the image $Z_\epsilon= f_\epsilon(\mathbb C^n)$ of perturbations $f_\epsilon$ of finite map-germs $f\colon (\mathbb C^n,0)\to(\mathbb C^p,0)$. Results in this field run parallel to the ones for Milnor fibrations of germs of complete intersections with isolated singularity (ICIS), but the highly singular nature of $Z_\epsilon$ imposes ob…