Topological equisingularity for isolated complete intersection singularities

Let X, x be a germ of an analytic variety (over the complex numbers) which is a complete intersection isolated singularity. The author associates to X, x a sequence µ∗= (µ0, µ1, . . . ) of numerical invariants by taking µi to be the minimal value of the Milnor numbers µ(Xi, xi) for all deformations (Xi, xi) → (Si, si) of X, x with dim Si = i. One has µ0 = µ(X, x) and µi = 0 if i is bigger than the embedding codimension of X, x. On the other hand the author defines the topological type of X, x as the class of homeomorphism of any sequence of germs (X, x) = (X0, x) ⊂ (X1, x) ⊂ ... ⊂ (Xk, x) where k is the embedding codimension of X, x, for each i, µ(Xi, x) = µi(X, x) and then the homeomorphism class does not depend on the Xi. The main result in the paper says that a µ∗-constant family of isolated complete intersection singularities of dimension different from two is topologically equisingular. A sufficient condition for the members of the family to have isomorphic monodromy fibrations is also given