Paper detail

The boundary of the Milnor fibre of complex and real analytic non-isolated singularities

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 given by the multiplication of f by the conjugate of g has an isolated critical value at 0. We give necessary and sufficient conditions for the real analytic map-germ 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 map-germs given by the multiplication of a holomorphic and a anti-holomorphic function defined in a complex surface germ, and we prove an A'Campo-type formula for the zeta function of their monodromy.