Abstract: It is a classical theorem in singularity theory that the variation operator associated with an isolated hypersurface singularity is an isomorphism between the relative homology and the absolute homology of the Milnor fiber. In this talk we introduce a homotopy version of this variation operator. Using the theory of framed mapping class groups for plane curve singularities, we give a complete criterion to decide if a set of disjoint properly embedded arcs is sent to a geometric vanishing cycle by this operator.