Cohomological connectivity of perturbations of map‐germs

Abstract

Let be a finite map‐germ with and the image of a small perturbation . We show that the reduced cohomology of is concentrated in a range of degrees determined by the dimension of the instability locus of f. In the case , we obtain an analogous result, replacing finiteness by ‐finiteness and by the discriminant . We also study the monodromy associated to the perturbation .