Linking numbers in three-manifolds (Q2046433)

The authors give an algorithm for computing the linking number of two rationally null homologous oriented simple closed curves in a connected, closed, oriented 3-manifold \(M\). The algorithm is given in terms of a presentation of \(M\) as an irregular dihedral three-fold cover of \(\mathbb{S}^3\) branched along a knot \(\alpha\) in \(\mathbb{S}^3\). This is no restriction since every connected, closed, oriented 3-manifold has such a presentation. They apply this result to evaluate one ribbon obstruction of the knot \(\alpha\).