Duality of linking pairing in Arnold's singularities (Q2378640)

The author shows a new aspect of the Arnold strange duality among 14 exceptional unimodal surface singularities. Every normal complex surface singularity \(X\) has a neighborhood which is the cone on a closed oriented 3-manifold \(M_X\) called the link. We have the linking pairing \(\lambda_{X}\) on the torsion part of the homology group \(H_1(M_X,\mathbb Z)\). The main result of the paper is that for unimodal singularities \(X\) and \(X^*\) which are dual in Arnold's sense, \(\lambda_{X}=-\lambda_{X^*}\). The result is proved by concrete calculation of the pairing.