Infinite order of the monodromy for all non–rational double point surface singularities

Establish that for any isolated hypersurface singularity X = V(f) in complex dimension n = 2 that is not a rational double point (ADE) singularity, the monodromy diffeomorphism of the Milnor fibration of f has infinite order in the smooth mapping class group π0(Diff(M, ∂)), where M is the Milnor fiber.

Background

The authors prove that for weighted-homogeneous isolated hypersurface surface singularities (n=2), the monodromy has infinite order in π0(Diff(M, ∂)) unless the singularity is a rational double point (ADE). This gives a differential-topological explanation of the failure of simultaneous resolution when the geometric genus pg>0. They then propose extending this conclusion beyond the weighted-homogeneous case.

This conjecture asserts that the infinite-order property should hold for all isolated hypersurface surface singularities that are not rational double points, removing the weighted-homogeneous hypothesis.