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Splice diagrams and universal abelian covers

Helge Møller Pedersen
(Ruprechts-Karls-Universität Heidelberg)
Seminar
Tuesday, 31 August, 2010, at 16:15-17:15, in Aud. D3 (1531-215)
Abstract:
Splice diagrams are used in the study of graph 3 manifolds, and is in particular importance for manifolds which are the link of a isolated complex surfaces singularity, they were first introduced by Eisenbud and Neumann in the case of integer homology sphere Graph manifolds. It was later extend to the study of graph manifolds 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 manifold. 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.
Organised by: CTQM/QGM
Contact person: Jørgen Ellegaard Andersen