Séminaire de topologie, géométrie et algèbre

I will present my recent joint work with J. F. de Bobadilla, proving that a family of isolated hypersurface singularities with constant Milnor number has constant multiplicity. The key idea is to endow the A'Campo model of "radius zero" monodromy with a symplectic structure. More precisely, I will construct a smooth manifold, fibered over an annulus, together with a fiberwise symplectic form such that the following holds. Over the outer circle ("positive radius"), we get the usual Milnor fibration.