  Earlier it was described to which extent the Alexander polynomial in several
variables of an algebraic link in the Poincar\'e sphere determines the topology
of the link. It was shown that, except some explicitly described cases, the
Alexander polynomial of an algebraic link determines the combinatorial type of
the minimal resolution of the curve and therefore the topology of the
corresponding link. The Alexander polynomial of an algebraic link in the
Poincar\'e sphere coincides with the Poincar\'e series of the corresponding set
of curve valuations. The latter one can be defined as an integral over the
space of divisors on the $E_8$-singularity. Here we consider a similar integral
for rational double point surface singularities over the space of Weil divisors
called the Weil-Poincar\'e series. We show that, except a few explicitly
described cases the Weil-Poincar\'e series of a collection of curve valuations
on a rational double point surface singularity determines the topology of the
corresponding link. We give analogous statements for collections of divisorial
valuations.
