Helge Moeller Pedersen (IML) – Splice diagrams and universal abelian covers of isolated surface singularities

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Date(s) - 20 octobre 2011

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Splice diagrams where first introduced by Eisenbud and Neumann in the study of isolated surface singularities with integer homology sphere link. It was later extend to the study of surface singularities with rational homology sphere link by Neumann and Wahl. They among other thing introduced a set of equations, called splice diagram equations, defined from the splice diagram, provided it satisfy the semigroup condition. They then went on to show that under a further condition on the manifold, the link of the splice diagram equation determines the universal abelian cover of the original singularity. I have shown that the splice diagram always determine the topology of the universal abelian cover. To do so I had to generalize to orbifolds, this also leads to an other condition, which is weaker than Neumann and Wahl’s, that imply that the splice diagram equation determines the universal abelian cover. This condition is for example always satisfied if one have a two node splice diagram satisfying the semigroup condition.