Splice diagram determining singularity links and universal abelian covers

Details Splice diagram determining singularity links and universal abelian covers Splice diagram determining singularity links and universal abelian covers

2008-11-13

arxiv.org/abs/0811.2213v2

Mathematics

Geometric Topology

Scientific paper

To a rational homology sphere graph manifold one can associate a weighted tree invariant called splice diagram. In this article 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.

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