The integral homology sphere conjecture for k-Lê–Yomdin singularities

Let $S$ be a $k$-Lê–Yomdin singularity with $k>1$, and consider its link.

Integral homology sphere conjecture. No $k$-Lê–Yomdin singularity with $k>1$ has an integral homology sphere link.

The conjecture is motivated by the absence of a closed formula for the determinant of a cyclic singularity and by experimentation. The source gives no proof or resolution.