The universal abelian cover of a graph manifold

Journal of Singularities
volume 7 (2013), 205-219

Received: 3 January 2013. Received in revised form: 6 May 2013

DOI: 10.5427/jsing.2013.7k

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Abstract:

Complex surfaces singularities with rational homology sphere links play an important role in singularity theory. They include all rational and splice quotient singularities, and in particular in the latter case the universal abelian cover of the link is a key element of the theory. All such links of singularities are graph manifolds, and to a rational homology sphere graph manifold one can associate a weighted tree invariant called splice diagram. It is known that the splice diagram determines the universal abelian cover of the manifold. In this paper we give an explicit method for constructing the universal abelian cover from the splice diagram, which works for most of the graph manifolds in particular for all links of singularities.

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