Finite-order monodromy in higher dimensions for n = 3 or 4

Determine whether, for n = 3 or n = 4, the monodromy ψ of an n-dimensional weighted-homogeneous isolated hypersurface singularity V = {f = 0} ⊂ ℂ^{n+1} whose link Y is an integral homology (2n−1)-sphere has finite order in the smooth mapping class group MCG(M) of a Milnor fiber M.

Background

The authors show that for n > 4, under the integral homology sphere link assumption, the monodromy has finite order in the smooth mapping class group. They also note that for n = 2, the phenomenon fails (monodromy can have infinite order).

However, the cases n = 3 and n = 4 remain unresolved, and clarifying whether the finite-order conclusion extends to these dimensions is posed explicitly as unknown.