Rational Homology Spheres as Universal Abelian Covers

Rational homology sphere graph manifolds play an important role in singularity theory. They occur as the links, and hence determine the topology, of many interesting types of surface singularities. These include all rational and splice quotient singularities. It is known that the splice diagram of a rational homology sphere graph manifold determines the universal abelian cover of the manifold. In this article, we give a condition on the splice diagram to determine when the universal abelian cover itself is a rational homology sphere.