Splice diagrams. Singularity links and universal abelian covers

To a rational homology sphere graph manifold one can associate a weighted tree invariant called splice diagram. In this thesis we prove a sufficient numerical condition on the splice diagram for a graph manifold to be a singularity link. We also show that if two manifolds have the same splice diagram, then their universal abelian covers are homeomorphic. To prove the last theorem we have to generalize our notions to orbifolds.