Abstract. Let f and g be holomorphic function-germs vanishing at the origin of a complex analytic germ of dimension three. Suppose that they have no common irreducible component and that the real analytic map-germ fḡ has an isolated critical value at 0. We give necessary and sufficient conditions for the real analytic map-germ fḡ to have a Milnor fibration and we prove that in this case the boundary of its Milnor fibre is a Waldhausen manifold. As an intermediate milestone we describe geometrically the Milnor fibre of mapgerms of the form fḡ defined in a complex surface germ, and we prove an A'Campo-type formula for the zeta function of its monodromy.

In this paper, we study the topology of real analytic map‐germs with isolated critical value f:false(double-struckRm,0false)→false(double-struckRn,0false), with 1

We study real analytic isolated singularities of type f:false(Cn+m+1,0false)→false(double-struckC,0false) with ffalse(z,wfalse)=gfalse(zfalse)+∑i=1m+1hifalse(wi,w¯ifalse), where g is holomorphic and each hi is a mixed polynomial, with z=(z1,⋯,zn) and w=(w1,⋯,wm+1). We construct a Lê's vanishing polyhedron for f, which describes the degeneration of its Milnor fiber Ff to the singular fiber. Then we prove that Ff is homotopy equivalent to the join Fg∗Fh1∗⋯∗Fhm+1, where Fg is the Milnor fiber of g and Fhi is the Milnor fiber of hi. This implies that Ff has the homotopy type of a bouquet of spheres Sn+m. So we can define the Milnor number μ(f) as the number of spheres in that bouquet, as in the complex setting.

No abstract

Let (X, 0) be the germ of either a subanalytic set or a complex analytic space , and let be a ‐analytic map‐germ, with or , respectively. When , there is a well‐known topological locally trivial fibration associated with f, called the Milnor–Lê fibration of f, which is one of the main pillars in the study of singularities of maps and spaces. However, when that is not always the case. In this paper, we give conditions which guarantee that the image of f is well‐defined as a set‐germ, and that f admits a Milnor–Lê fibration. We also give conditions for f to have the Thom property. Finally, we apply our results to mixed function‐germs of type on a complex analytic surface with arbitrary singularity.