Variation mappings on singularities with a 1-dimensional critical locus (Q1814439)

Let \(f:(\mathbb{C}^{n+1},0)\to(\mathbb{C},0)\) be a germ of an analytic function with a 1-dimensional singular locus \(\sigma=\sigma_ 1\cup\dots\cup\sigma_ r\), \(\sigma_ i\) irreducible curves. Let \(F\) be the Milnor fibre of \(f\) and \(F_ i\) the Milnor fibres of the germ of a generic transversal section at \(x\in\sigma_ i\setminus\{0\}\). This way one obtains several monodromy actions on the corresponding homology group. The aim of the paper is to study these monodromies to understand the topology of this class of singularities.