Generalized infinite-order monodromy conjecture for surface singularity smoothings

Let $(V,p)$ be a normal isolated surface singularity with rational homology $3$-sphere link, and let it have a smoothing with Milnor fiber $M$ and monodromy $\psi$. Suppose that $\psi$ acts with finite order on $H_\ast(M,\mathbb{Z})$. Let $p_g(V,p)$ denote the geometric genus of the singularity. Generalized infinite-order monodromy conjecture. The monodromy $\psi$ has infinite order in the smooth mapping class group $\operatorname{MCG}(M)\,$ when $p_g(V,p)>0$. This generalizes the hypersurface case and is motivated by examples for equivariant smoothings of quasi-homogeneous minimally elliptic surface singularities; the proposition in the paper gives finite order in the topological mapping class group under the stated homological hypothesis, while the smooth assertion remains open.