  For the link $M$ of a normal complex surface singularity $(X,0)$ we ask when
a knot $K\subset M$ exists for which the answer to whether $K$ is the link of
the zero set of some analytic germ $(X,0)\to (\mathbb C,0)$ affects the
analytic structure on $(X,0)$. We show that if $M$ is an integral homology
sphere then such a knot exists if and only if $M$ is not one of the Brieskorn
homology spheres $M(2,3,5)$, $M(2,3,7)$, $M(2,3,11)$.
