Splice diagram determining singularity links and universal abelian covers

摘要

To a rational homology sphere graph manifold one can associate a weightedtree invariant called splice diagram. In this article we prove a sufficientnumerical condition on the splice diagram for a graph manifold to be asingularity link. We also show that if two manifolds have the same splicediagram, then their universal abelian covers are homeomorphic. To prove thelast theorem we have to generalize our notions to orbifolds.