Splice diagram determining singularity links and universal abelian covers

2008/11/13 by Helge Møller Pedersen, Pedersen, Helge Møller
Computer Science · Mathematics · #32S28 #32S50 #57M10 #57M27 #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Polynomial and algebraic computation #math.GT #msc:32S28 #msc:32S50 #msc:57M10 #msc:57M27

paper · pdf · doi:10.48550/arxiv.0811.2213

openalex publication_date 2008/11/13 · arxiv created 2008/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Constructing Universal Abelian Covers of Graph Manifolds
• Splice Diagram Singularities and The Universal Abelian Cover of Graph Orbifolds
• Determining When The Universal Abelian Cover of a Graph Manifold is a Rationla Homology Sphere
• Splice diagrams and splice-quotient surface singularities
• Topology, geometry, and equations of normal surface singularities