Determining When The Universal Abelian Cover of a Graph Manifold is a Rationla Homology Sphere

TL;DR

This paper provides a criterion based on splice diagrams to identify when the universal abelian cover of a graph manifold is a rational homology sphere, building on previous work linking splice diagrams to manifold covers.

Contribution

It introduces a specific condition on splice diagrams that determines when the universal abelian cover is a rational homology sphere, extending prior results.

Findings

A new splice diagram condition for rational homology sphere covers

Characterization of universal abelian covers as rational homology spheres

Extension of previous results linking splice diagrams and manifold covers

Abstract

It was shown in my earlier article that the splice diagram of a rational homology sphere graph manifold determines the manifolds universal abelian cover. In this article we use the proof of this to give a condition on the splice diagram to determine when the universal abelian cover itself is a rational homology sphere.