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We show that every family of isolated hypersurface singularity with constantMilnor number has constant multiplicity. To achieve this, we endow the A'Campomodel of "radius zero" monodromy with a symplectic structure. This new approachallows to generalize a spectral sequence of McLean converging to fixed pointFloer homology of iterates of the monodromy to a more general setting which iswell suited to study $\mu$-constant families.

Symplectic monodromy at radius zero and equimultiplicity of $\mu$-constant families