Abstract
We show that every family of isolated hypersurface singularities with constant Milnor number has constant multiplicity. To achieve this, we endow the A’Campo model of “radius zero” monodromy with a symplectic structure. This new approach allows to generalize a spectral sequence of McLean converging to fixed point Floer homology of iterates of the monodromy to a more general setting which is well suited to study $\mu$-constant families.
