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

de Bobadilla, Javier Fernandez and Menegon, Neto A (2014) The boundary of the Milnor fibre of complex and real analytic non-isolated singularities. GEOMETRIAE DEDICATA, 173 (1). pp. 143-162. ISSN 0046-5755

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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 fg¯ has an isolated critical value at 0. We give necessary and sufficient conditions for the real analytic map-germ fg¯ 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 fg¯ defined in a complex surface germ, and we prove an A’Campo-type formula for the zeta function of its monodromy.

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